"Проблемы прочности", 2008, № 1 (для печати)

ÏÐÎÁËÅÌÛ
ÏÐÎ×ÍÎÑÒÈ
Ìåæäóíàðîäíûé
íàó÷íî-òåõíè÷åñêèé æóðíàë
Îñíîâàí â èþëå 1969 ã.
¹ 1 (391) — 2008 ã.
Ó÷ðåäèòåëè: Íàöèîíàëüíàÿ àêàäåìèÿ íàóê Óêðàèíû
Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû
(Ðåãèñòðàöèîííîå ñâèäåòåëüñòâî ñåðèÿ ÊÂ ¹ 129 îò 07. 10. 1993 ã.)
Èçäàòåëü: Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû
Ðåäàêöèîííàÿ êîëëåãèÿ:
Â. Ò. Òðîùåíêî (ãëàâíûé ðåäàêòîð), Á. À. Ãðÿçíîâ, À. Ë. Êâèòêà, Á. È.
Êîâàëü÷óê, Ë. Â. Êðàâ÷óê, À. ß. Êðàñîâñêèé, Â. Â. Êðèâåíþê, À. À.
Ëåáåäåâ, Ï. Ï. Ëåïèõèí, Â. Â. Ìàòâååâ, Â. Ï. Íàóìåíêî, Ã. Â. Ñòåïàíîâ,
Â. À. Ñòðèæàëî (çàì. ãëàâíîãî ðåäàêòîðà),Â.Â.Õàð÷åíêî,Â.Ê.Õàð÷åíêî
(çàì. ãëàâíîãî ðåäàêòîðà), À. Ï. ßêîâëåâ
Ðåäàêöèîííûé ñîâåò:
Ñ. Âîäåíè÷àðîâ (Áîëãàðèÿ), À. Êàðïèíòåðè (Èòàëèÿ), Äæ. Ä. Ëàíäåñ
(ÑØÀ), Ý. Ìàõà (Ïîëüøà), Í. À. Ìàõóòîâ (Ðîññèÿ), Í. Ô. Ìîðîçîâ
(Ðîññèÿ), Þ. Ìóðàêàìè (ßïîíèÿ), Â. Íîâàöêèé (Ïîëüøà), Ã. Ïëþâèíàæ
(Ôðàíöèÿ), ß. Ïîêëóäà (×åõèÿ), Ð. Ñàíäåð (Èíäèÿ), Ñ. Ñåäìàê
(Ñåðáèÿ), Ë. Òîò (Âåíãðèÿ), Ä. Ôðàíñóà (Ôðàíöèÿ), Ê. Â. Ôðîëîâ
(Ðîññèÿ)
Ðåäàêöèÿ æóðíàëà «Ïðîáëåìû ïðî÷íîñòè»:
À. Î. Õîöÿíîâñêèé (îòâ. ñåêðåòàðü)
Â. Â. Íàóìåíêî (çàâ. ðåä.-èçä. îòäåëîì)
Ë. Á. Äåäóõ (âåä. ðåäàêòîð)
Í. Ì. Øèíêàðåíêî (êîððåêòîð)
Àäðåñ ðåäàêöèè: 01014, Êèåâ–14, óë. Òèìèðÿçåâñêàÿ, 2
Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî
Íàöèîíàëüíîé àêàäåìèè íàóê Óêðàèíû
Òåëåôîí: (044) 286 5657
Ôàêñ: (044) 286 1684
E-mail:
Æóðíàë ïåðåâîäèòñÿ íà àíãëèéñêèé ÿçûê è èçäàåòñÿ ïîä íàçâàíèåì «Strength of Materials»
ñ 1969 ã. èçäàòåëüñòâîì Plenum Publishing Corporation, ñ 2004 ã. Springer Science +
Business Media, Inc.
© Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû, 2008

PROBLEMS
of STRENGTH
International
scientific & technical journal
founded in July 1969
No. 1 (391) — 2008
Founders: National Academy of Sciences of Ukraine
Pisarenko Institute of Problems of Strength, National Academy of Sciences
of Ukraine
Publisher: Pisarenko Institute of Problems of Strength, National Academy of Sciences
of Ukraine
Editorial board:
V. Ò. Òroshchenko (editor-in-chief), B. À. Gryaznov, V. Ê. Kharchenko (associate
editor), V. V. Kharchenko, B. I. Êîvàl’chuk, À. Ya. Krasovskii, L. V. Êràvchuk,
V. V. Êrivenyuk, À. L. Êvitka, À. À. Lebedev, P. P. Lepikhin, V. V. Ìàtvååv,
V. P. Nàumånkî, G. V. Ståpànîv, V. À. Strizhalo (associate editor), À. P. Yakovlev
Advisory board:
A. Carpinteri (Italy), D. Francois (France),Ê.V.Frîlîv(Russia),J.D.Landes
(USA), E. Macha (Poland), N. À. Ìàkhutîv (Russia), N. F. Morozov (Russia),
Y. Murakami (Japan), W. Nowacki (Poland), G. Pluvinage (France), J. Pokluda
(Czech Republik), S. Sedmak (Serbia), R. Sunder (India), L. Toth (Hungary),
S. Vodenicharov (Bulgaria)
Editorial staff:
A. O. Khotsyanovskii, V. V. Naumenko,
L. B. Dedukh, N. M. Shinkarenko
Address: Pisarenko Institute of Problems of Strength
2, Timiryazevskaya str., Kiev, 01014, Ukraine
Telephone: (044) 286 5657
Fax: (044) 286 1684
E-mail:
The Journal has been translated into English and published under the title Strength of
Materials since 1969 by Plenum Publishing Corporation, and since 2004 by Springer
Science + Business Media, Inc.
© Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, 2008

Ñîäåðæàíèå
Ïðåäèñëîâèå .................................................................................................................................................. 7
Íàó÷íî-òåõíè÷åñêèé ðàçäåë
ÓÌÅÍÎ É., ÊÈÍÎÑÈÒÀ Þ., ÊÈÒÀÌÓÐÀ Ò. Ab initio èññëåäîâàíèÿ èäåàëüíîãî ïðåäåëà ïðî÷íîñòè
íà ñäâèã ïîëèòèïîâ êàðáèäà êðåìíèÿ íà îñíîâå ôóíêöèîíàëüíîé òåîðèè ïëîòíîñòè (íà àíãë.
ÿç.) .................................................................................................................................................................... 8
ÁÎÌÀÑ Õ., ÊÈÍÖËÅÐ Ð., ÊÓÍÎÂ Ñ., ËÅÂÈØ Ã., ØÐÅÄÅÐ Ð. Çàðîæäåíèå òðåùèí è ïðåäåë
âûíîñëèâîñòè òâåðäûõ ñòàëåé ïðè ìíîãîîñíûõ öèêëè÷åñêèõ íàãðóçêàõ (íà àíãë. ÿç.) ......................... 14
ØÅÑÒÀÊ Ï., ×ÅÐÍÛ Ì., ÏÎÊËÓÄÀ ß. Èññëåäîâàíèå óïðóãèõ ñâîéñòâ ñòðóêòóðû B19’ ñïëàâà
NiTi ïðè îäíîîñíîì è ãèäðîñòàòè÷åñêîì íàãðóæåíèè ïðè èñïîëüçîâàíèè ìåòîäà ab initio (íà àíãë.
ÿç.) .................................................................................................................................................................... 20
ÞÐÈÊÎÂÀ À., MÈØÊÓÔ É., ×ÀÕ K., OÖÅËÈÊ Â. Ñòðóêòóðíûå èçìåíåíèÿ âñëåäñòâèå ïîëçó-
÷åñòè â àìîðôíîì ñïëàâå Ni–Si–B (íà àíãë. ÿç.) ........................................................................................ 24
ÌÈØÊÓÔ É., ×ÀÕ Ê., ÞÐÈÊÎÂÀ À., ÎÖÅËÈÊ Â., ÁÅÍÃÓÑ Â., ÒÀÁÀ×ÍÈÊÎÂÀ Å. Ðàçðóøåíèå
àìîðôíîé ìåòàëëè÷åñêîé ëåíòû èç Zr50Ti16.5Cu15Ni18.5 (íà àíãë. ÿç.) ....................................................... 28
ÄÛÌÀ×ÅÊ Ï., ÌÈËÈ×ÊÀ Ê. Èñïûòàíèÿ íà èçãèá ìàëûõ îáðàçöîâ è èõ ÷èñëåííîå ìîäåëèðîâàíèå
â óñëîâèÿõ ïîñòîÿííîãî èçãèáàþùåãî óñèëèÿ (íà àíãë. ÿç.) ...................................................... 32
ÌÈËÈ×ÊÀ Ê., ÄÎÁÅØ Ô. Îïèñàíèå êðèâûõ ïîëçó÷åñòè äëÿ ñïëàâà Mg–4Al–1Ca (íà àíãë. ÿç.) ... 36
ÇÀÏËÅÒÀË É., ÂÅ×ÅÒ Ñ., ÊÎÃÓÒ ß., ÎÁÐÒËÈÊ Ê. Óñòàëîñòíàÿ äîëãîâå÷íîñòü èçîòåðìè÷åñêè
îòïóùåííîãî êîâêîãî ÷óãóíà â èíòåðâàëå îò ïðåäåëà ïðî÷íîñòè ïðè ðàñòÿæåíèè äî óñòîé÷èâîãî
ïðåäåëà âûíîñëèâîñòè (íà àíãë. ÿç.) .................................................................................................................. 40
ÑÓÕÀÍÅÊ Ï., ØÈÍÄËÅÐ È., KÐÀÒÎÕÂÈË Ï., ÃÀÍÓÑ Ï. Ñîïðîòèâëåíèå äåôîðìèðîâàíèþ è
ïðîöåññû ñòðóêòóðîîáðàçîâàíèÿ àëþìèíèäîâ æåëåçà ïðè ãîðÿ÷åé ïðîêàòêå (íà àíãë. ÿç.) ................. 44
ÑÅÄËÀ×ÅÊ ß., ÕÓÌÀÐ À. Àíàëèç ìåõàíèçìîâ ðàçðóøåíèÿ è êà÷åñòâà ïîâåðõíîñòè êîìïîçèöèîííûõ
ìàòåðèàëîâ ïðè ñâåðëåíèè (íà àíãë. ÿç.) .................................................................................... 48
ÇÀÐÈÊÎÂÑÊÀß Í. Â., ÇÓÅ Ë. Á. Ëîêàëèçàöèÿ ïëàñòè÷åñêîé äåôîðìàöèè è ðàçðóøåíèå ïîëèêðèñòàëëîâ
àëþìèíèÿ (íà àíãë. ÿç.) ............................................................................................................. 52
ØÓÊÀÅ Ñ., ÃËÀÄÑÊÈÉ Ì., ÇÀÕÎÂÀÉÊÎ À., ÏÀÍÀÑÎÂÑÊÈÉ Ê. Ìåòîä îöåíêè äîëãîâå÷íîñòè
ìåòàëëè÷åñêèõ ìàòåðèàëîâ ïðè ìàëîöèêëîâîé óñòàëîñòè â óñëîâèÿõ ìíîãîîñíîãî íàãðóæåíèÿ
(íà àíãë. ÿç.) ........................................................................................................................................ 56
ØÈÍÄËÅÐ È., ÑÓÕÀÍÅÊ Ï., ÐÓØ Ñ., ÊÓÁÅ×ÊÀ Ï., ÑÎÉÊÀ ß., ÕÅÃÅÐ Ì., ËÈØÊÀ Ì.,
ÕËÈÑÍÈÊÎÂÑÊÈ Ì. Îöåíêà îáðàçîâàíèÿ ãîðÿ÷èõ òðåùèí â âûñîêîëåãèðîâàííûõ ñòàëÿõ ìåòîäîì
ïðîêàòêè íà êëèí (íà àíãë. ÿç.) .............................................................................................................. 60
ÁÅÐÊÀ Ë. Î ìåõàíèêå äåôîðìèðîâàíèÿ è ïðîöåññàõ äðîáëåíèÿ (íà àíãë. ÿç.) ...................................... 64
ÊÀÐÎËÜ×ÓÊ À., ÌÀÕÀ Ý. Îáúåìíûé è òî÷å÷íûé ïîäõîäû ïðè îöåíêå óñòàëîñòíîé äîëãîâå÷íîñòè
â óñëîâèÿõ ñîâìåñòíîãî íàãðóæåíèÿ ïðè èçãèáå è êðó÷åíèè (íà àíãë. ÿç.) ............................ 69
ÌÀÉÎÐ Ø., ÏÀÏÓÃÀ ß., ÕÎÐÍÈÊÎÂÀ ß., ÏÎÊËÓÄÀ ß. Ñðàâíåíèå êðèòåðèåâ óñòàëîñòè ïðè
ñîâìåñòíîì èçãèáå è êðó÷åíèè äëÿ àçîòèðîâàííûõ îáðàçöîâ è îáðàçöîâ â èñõîäíîì ñîñòîÿíèè (íà
àíãë. ÿç.) .......................................................................................................................................................... 73
ÌÐÀÇÊÎÂÀ Ë., ËÀÓØÌÀÍÍ Õ. Êîëè÷åñòâåííûé ôðàêòîãðàôè÷åñêèé àíàëèç ïîâåðõíîñòåé
óäàðíîãî ðàçðóøåíèÿ ñòàëè R73 (íà àíãë. ÿç.) ............................................................................................ 77
TAÁÀ×ÍÈÊÎÂÀ E. Ä., ÏÎÄÎËÜÑÊÈÉ A. Â., ÁÅÍÃÓÑ Â. Ç., ÑÌÈÐÍΠÑ. Í., ×ÀÕ Ê.,
MÈØÊÓÔ É., ÑÀÈÒÎÂÀ Ë. Ð., ÑÅÌÅÍÎÂÀ È. Ï., ÂÀËÈÅÂ Ð. Ç. Îñîáåííîñòè ìèêðîñòðóêòóðû
ïîâåðõíîñòåé èçëîìà è íèçêîòåìïåðàòóðíûå ìåõàíè÷åñêèå ñâîéñòâà ñâåðõìåëêîçåðíèñòîãî ELIñïëàâà
Ti–6Al–4V (íà àíãë. ÿç.) .................................................................................................................... 81
ÊÎÍÅ×ÍÀ Ð., ÍÈÊÎËÅÒÒÎ Äæ., ÌÀÉÅÐÎÂÀ Â., ÁÀÉ×È Ï. Âëèÿíèå àçîòèðîâàíèÿ íà õàðàêòåðèñòèêè
óñòàëîñòè è ìèêðîìåõàíèçìû ðàçðóøåíèÿ ÷óãóíà ñ øàðîâèäíûì ãðàôèòîì (íà àíãë. ÿç.) 85
ÊÎÂÀÐÈÊ Î., ÑÈÃË ß. Ìèêðîñòðóêòóðà è ìîðôîëîãèÿ ïîâåðõíîñòè èçëîìà ãàçîòåðìè÷åñêèõ
ïîêðûòèé èç òóãîïëàâêèõ ìåòàëëîâ è êåðàìèêè (íà àíãë. ÿç.) .................................................................. 89
ÊÀÖ Þ., ÒÛÌßÊ Í., ÃÅÐÁÅÐÈÕ Â. Â. Ïðèïîâåðõíîñòíàÿ ìîäèôèêàöèÿ â ðåçóëüòàòå âçàèìîäåéñòâèÿ
ñ âîäîðîäîì: ãëîáàëüíûé è ëîêàëüíûé ïîäõîäû (íà àíãë. ÿç.) ................................................ 93
KOÒÀË Â., ÑÒÎÏÊÀ Ï., ÑÀÉÄË Ï., ØÂÎÐ×ÈÊ Â. Èçó÷åíèå òîíêîãî ïîâåðõíîñòíîãî ñëîÿ
ïîëèýòèëåíà ïîñëå ïëàçìåííîé îáðàáîòêè (íà àíãë. ÿç.) ........................................................................... 97

ÏËÅÕΠO., ÓÂÀÐΠÑ., ÍÅÉÌÀÐÊ O. Òåîðåòè÷åñêîå è ýêñïåðèìåíòàëüíîå èññëåäîâàíèå
ñîîòíîøåíèÿ ðàññåÿííîé è íàêîïëåííîé ýíåðãèè â æåëåçå ïðè êâàçèñòàòè÷åñêîì è öèêëè÷åñêîì
íàãðóæåíèè (íà àíãë. ÿç.) .............................................................................................................................. 101
ÍÅÉÌÀÐÊ O., ÏËÅÕÎÂ O., ÏÐÀÓÄ Â., ÓÂÀÐÎÂ Ñ. Êîëëåêòèâíûå êîëåáàíèÿ ìíîæåñòâà ìèêðîñäâèãîâ
êàê ìåõàíèçì âîëíû ðàçðóøåíèÿ (íà àíãë. ÿç.) ............................................................................ 105
ÏÀÍÓØÊÎÂÀ Ì., ÒÈËËÎÂÀ Å., ÕÀËÓÏÎÂÀ Ì. Çàâèñèìîñòü ìåõàíè÷åñêèõ ñâîéñòâ ëèòîãî
àëþìèíèåâîãî ñïëàâà AlSi9Cu3 îò åãî ìèêðîñòðóêòóðû (íà àíãë. ÿç.) ................................................... 109
ÂÀËÅÊ Ø., ÕÀÓØÈËÄ Ï., ÊÛÒÊÀ Ì. Ìåõàíèçìû ðàçðóøåíèÿ îáëó÷åííîé íåéòðîíàìè ñòàëè
15Õ2ÌÔÀ (íà àíãë. ÿç.) ................................................................................................................................ 113
ÄÎÁÅØ Ô., ÊÐÀÒÎÕÂÈË Ï., ÌÈËÈ×ÊÀ Ê. Ïîëçó÷åñòü ïðè ñæàòèè àëþìèíèäà æåëåçà òèïà
Fe3Al ñ äîáàâêàìè Zr (íà àíãë. ÿç.) ............................................................................................................... 117
ÐÎÇÓÌÅÊ Ä. Ðîñò òðåùèí â ñòàëè FeP04 ïðè öèêëè÷åñêîì ðàñòÿæåíèè è ðàçëè÷íîé ôîðìå
íàäðåçîâ ñ ó÷åòîì åå ìèêðîñòðóêòóðû (íà àíãë. ÿç.) ................................................................................. 121
ÄÎÁÅØ Ô., ÏÅÐÅÑ Ï., ÌÈËÈ×ÊÀ Ê., ÃÀÐÊÅÑ Ã., ÀÄÅÂÀ Ï. Îöåíêà àíèçîòðîïèè ìåõàíè÷åñêèõ
ñâîéñòâ ìàãíèåâûõ ñïëàâîâ ñ ïîìîùüþ èñïûòàíèé íà ïîëçó÷åñòü ïðè ñæàòèè (íà àíãë. ÿç.) .............. 125
ÊÀÄËÅÖ ß., ÄÂÎÐÀÊ Ì. Ïîâåðõíîñòíàÿ îáðàáîòêà íåðæàâåþùåé ñòàëè X12CrNi 18 8 (íà àíãë.
ÿç.) .................................................................................................................................................................... 129
ÄÛß Ä., ÑÒÐÀÄÎÌÑÊÈ Ç., ÏÈÐÅÊ À. Àíàëèç ìèêðîñòðóêòóðû è ðàçðóøåíèÿ ñîñòàðåííîé ëèòîé
äâóõôàçíîé ñòàëè (íà àíãë. ÿç.) .................................................................................................................... 133
ÑÒÐÀÄÎÌÑÊÈ Ç., ÄÛß Ä., ÏÈÐÅÊ À. Âëèÿíèå ìîðôîëîãèè êàðáèäîâ íà âÿçêîñòü ðàçðóøåíèÿ
ëèòîé ñòàëè G200CrMoNi4-3-3 (íà àíãë. ÿç.) .............................................................................................. 137
ÓÅÌÀÖÓ É., ÒÎÊÀÉÈ Ê., ÎÕÀØÈ Ò. Êîððîçèîííàÿ óñòàëîñòü ýêñòðóçèîííûõ ìàãíèåâûõ
ñïëàâîâ AZ80, AZ61 è AM60 â äèñòèëëèðîâàííîé âîäå (íà àíãë. ÿç.) .................................................... 141
ÍÅÇÁÅÄÎÂÀ Å., ÔÈÄËÅÐ Ë., ÌÀÉÅÐ Ç., ÂËÀÕ Á., ÊÍÅÑË Ç. Òðåùèíîñòîéêîñòü ìíîãîñëîéíûõ
òðóá (íà àíãë. ÿç.) ........................................................................................................................................... 146
ÓÅÌÀÖÓ É., ÒÎÇÀÊÈ ß., ÒÎÊÀÉÈ Ê., ÍÀÊÀÌÓÐÀ Ì. Óñòàëîñòü ñîåäèíåíèé, ïîëó÷åííûõ
ñâàðêîé òðåíèåì, ðàçëè÷íûõ àëþìèíèåâûõ ñïëàâîâ: ëèòûõ è îáðàáîòàííûõ äàâëåíèåì (íà àíãë.
ÿç.) .................................................................................................................................................................... 150
ÌÓØÀËÅÊ Ð., ÕÀÓØÈËÄ Ï., CÈÃË ß., ÁÅÍØ ß., ÑËÀÌÀ ß. Ìåõàíè÷åñêèå ñâîéñòâà è
îñîáåííîñòè ðàçðóøåíèÿ âûñîêîïðî÷íûõ ñòàëåé (íà àíãë. ÿç.) ............................................................... 155
ßÊÎÁÑÎÍ Ë., ÏÅÐÑÑÎÍ Õ., ÌÅËÈÍ Ñ. Èññëåäîâàíèå in situ ðîñòà óñòàëîñòíîé òðåùèíû ñ
ïîìîùüþ ýëåêòðîííîãî ñêàíèðóþùåãî ìèêðîñêîïà (íà àíãë. ÿç.) .......................................................... 159
ÕÀÍÑÑÎÍ Ï., ÌÅËÈÍ Ñ. Èññëåäîâàíèå âëèÿíèÿ ãðàíèö çåðåí íà ðàçâèòèå êîðîòêèõ óñòàëîñòíûõ
òðåùèí ñ ïîìîùüþ ìåòîäà äèñêðåòíûõ äèñëîêàöèé (íà àíãë. ÿç.) ......................................................... 163
ÍÎÂÀÊ Ñ., ÎØÈÍ Ï., ÏÀÑÊÎ A., ÃÓÝÐÈÍ Ñ., ØÀÌÏÈÎÍ ß. Ìåõàíè÷åñêèå õàðàêòåðèñòèêè
âûñîêîïðî÷íûõ ñòåêîë íà îñíîâå öèðêîíèÿ (íà àíãë. ÿç.) ........................................................................ 167
ØÀÍßÂÑÊÈÉ À. À., ÏÎÒÀÏÅÍÊÎ Þ. À. Ìåõàíèçìû óñòàëîñòíîãî ðàçðóøåíèÿ äèñêîâ äâèãàòåëÿ
âåðòîëåòà ÒÂ3-117ÂÊ ïðè ýêñïëóàòàöèîííûõ íàãðóçêàõ (íà àíãë. ÿç.) .......................................... 171
Óòâåðæäåí ê ïå÷àòè ó÷åíûì ñîâåòîì ÈÏÏ èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû.
Íîìåð ïîäãîòîâëåí, íàáðàí è ñâåðñòàí â ðåäàêöèè ÈÏÏ èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû.
Îòïå÷àòàí â òèïîãðàôèè Èçäàòåëüñêîãî äîìà “Àêàäåìïåðèîäèêà”,
óë. Òåðåùåíêîâñêàÿ 4, 01004, Êèåâ-4. Çàêàç ¹ 2042.
Ïîäï. ê ïå÷àòè è â ñâåò 21. 01. 2008. Òèðàæ 570 ýêç. Öåíà äîãîâîðíàÿ.

Contents
Preface ............................................................................................................................................................ 7
Scientific and Technical Section
UMENO Y., KINOSHITA Y., and KITAMURA T. Ab Initio DFT Study of Ideal Shear Strength of
Polytypes of Silicon Carbide .......................................................................................................................... 8
BOMAS H., KIENZLER R., KUNOW S., LOEWISCH G., and SCHROEDER R. Crack Initiation and
Endurance Limit of Hard Steels under Multiaxial Cyclic Loads .................................................................... 14
ŠESTÁK P., ÈERNÝ M., and POKLUDA J. Elastic Properties of B19’ Structure of NiTi Alloy under
Uniaxial and Hydrostatic Loading from First Principles ................................................................................ 20
JURÍKOVÁ A., MIŠKUF J., CSACH K., and OCELÍK V. Creep-Induced Structural Changes in Ni–Si–B
Amorphous Alloy ............................................................................................................................................ 24
MIŠKUF J., CSACH K., JURÍKOVÁ A., OCELÍK V., BENGUS V., and TABACHNIKOVA E. Failure
of Zr50Ti16.5Cu15Ni18.5 Amorphous Metallic Ribbon ....................................................................................... 28
DYMÁÈEK P. and MILIÈKA K. Small Punch Testing and Its Numerical Simulations under Constant
Deflection Force Conditions ........................................................................................................................... 32
MILIÈKA K. and DOBEŠ F. Constitutive Description of Creep Behavior of Mg–4Al–1Ca Alloy ............. 36
ZAPLETAL J., VÌCHET S., KOHOUT J., and OBRTLÍK K. Fatigue Lifetime of ADI from Ultimate
Tensile Strength to Permanent Fatigue Limit ................................................................................................. 40
SUCHÁNEK P., SCHINDLER I., KRATOCHVÍL P., and HANUS P. Deformation Resistance and
Structure-Forming Processes of Iron Aluminides in Hot Rolling ..................................................................... 44
SEDLÁÈEK J. and HUMÁR A. Analysis of Fracture Mechanisms and Surface Quality in Drilling of
Composite Materials ....................................................................................................................................... 48
ZARIKOVSKAYA N. V. and ZUEV L. B. Localization of Plastic Deformation and Fracture in
Aluminum Polycrystals ................................................................................................................................... 52
SHUKAEV S., GLADSKII M., ZAKHOVAIKO A., and PANASOVSKII K. A Method for Low-Cycle
Fatigue Life Assessment of Metallic Materials under Multiaxial Loading .................................................... 56
SCHINDLER I., SUCHÁNEK P., RUSZ S., KUBEÈKA P., SOJKA J., HEGER M., LIŠKA M., and
HLISNÍKOVSKÝ M. Hot-Cracking of High-Alloyed Steels Evaluated by Wedge Rolling Test ....... 60
BERKA L. On Mechanics of Deformation and Crushing Processes .............................................................. 64
KAROLCZUK A. and MACHA E. Area and Point Approaches in Fatigue Life Evaluation under
Combined Bending and Torsion Loading ....................................................................................................... 69
MAJOR Š., PAPUGA J., HORNÍKOVÁ J., and POKLUDA J. Comparison of Fatigue Criteria for
Combined Bending–Torsion Loading of Nitrided and Virgin Specimens ..................................................... 73
MRÁZKOVÁ L. and LAUSCHMANN H. Quantitative Fractographic Analysis of Impact Fracture
Surfaces of Steel R73 ...................................................................................................................................... 77
TABACHNIKOVA E. D., PODOLSKIY A. V., BENGUS V. Z., SMIRNOV S. N., CSACH K.,
MIŠKUF J., SAITOVA L. R., SEMENOVA I. P., and VALIEV R. Z. Microstructural Features of Failure
Surfaces and Low-Temperature Mechanical Properties of Ti–6Al–4V ELI Ultra-Fine Grained Alloy ........ 81
KONEÈNÁ R., NICOLETTO G., MAJEROVÁ V., and BAICCHI P. Influence of Nitriding on the Fatigue
Behavior and Fracture Micromechanisms of Nodular Cast Iron ........................................................................ 85
KOVÁØÍK O. and SIEGL J. Microstructure and Fracture Morphology of Thermally Sprayed Refractory
Metals and Ceramics ....................................................................................................................................... 89
KATZ Y., TYMIAK N., and GERBERICH W. W. Near Surface Modification Affected by Hydrogen
Interaction: Global Supplemented by Local Approach .................................................................................. 93
KOTÁL V., STOPKA P., SAJDL P., and ŠVORÈÍK V. Thin Surface Layer of Plasma Treated
Polyethylene .................................................................................................................................................... 97
PLEKHOV O., UVAROV S., and NAIMARK O. Theoretical and Experimental Investigation of the
Dissipated and Stored Energy Ratio in Iron under Quasi-Static and Cyclic Loading .................................... 101
NAIMARK O., PLEKHOV O., PROUD W., and UVAROV S. Collective Modes in the Microshear
Ensemble as a Mechanism of the Failure Wave ............................................................................................. 105
PANUŠKOVÁ M., TILLOVÁ E., and CHALUPOVÁ M. Relation between Mechanical Properties and
Microstructure of Cast Aluminum Alloy AlSi9Cu3 ....................................................................................... 109

VÁLEK Š., HAUŠILD P., and KYTKA M. Mechanisms of Fracture in Neutron-Irradiated 15Ch2MFA
Steel ................................................................................................................................................................ 113
DOBEŠ F., KRATOCHVÍL P., and MILIÈKA K. Compressive Creep of Fe3Al-type Iron Aluminide with
Zr Additions .................................................................................................................................................... 117
ROZUMEK D. Crack Growth in FeP04 Steel under Cyclic Tension for Different Notches on the Basis of
its Microstructure ............................................................................................................................................ 121
DOBEŠ F., PÉREZ P., MILIÈKA K., GARCÉS G., and ADEVA P. Estimation of Anisotropy of
Mechanical Properties in Mg Alloys by Means of Compressive Creep Tests ............................................... 125
KADLEC J. and DVORAK M. Duplex Surface Treatment of Stainless Steel X12CrNi 18 8 ...................... 129
DYJA D., STRADOMSKI Z., and PIREK A. Microstructural and Fracture Analysis of Aged Cast Duplex
Steel ................................................................................................................................................................ 133
STRADOMSKI Z., PIREK A., and DYJA D. Influence of Carbides Morphology on Fracture Toughness
of Cast Steel G200CrMoNi4-3-3 .................................................................................................................... 137
UEMATSU Y., TOKAJI K., and OHASHI T. Corrosion Fatigue Behavior of Extruded AZ80, AZ61, and
AM60 Magnesium Alloys in Distilled Water ................................................................................................. 141
NEZBEDOVÁ E., FIEDLER L., MAJER Z., VLACH B., and KNÉSL Z. Fracture Toughness of
Multilayer Pipes .............................................................................................................................................. 146
UEMATSU Y., TOZAKI Y., TOKAJI K., and NAKAMURA M. Fatigue Behavior of Dissimilar Friction
Stir Welds between Cast and Wrought Aluminum Alloys ............................................................................. 150
MUŠÁLEK R., HAUŠILD P., SIEGL J., BENSCH J., and SLÁMA J. Mechanical Properties and
Fracture Behavior of High-Strength Steels ..................................................................................................... 155
JACOBSSON L., PERSSON C., and MELIN S. In Situ Scanning Electron Microscopy Study of Fatigue
Crack Propagation ........................................................................................................................................... 159
HANSSON P. and MELIN S. Grain Boundary Influence during Short Fatigue Crack Growth Using a
Discrete Dislocation Technique ...................................................................................................................... 163
NOWAK S., OCHIN P., PASKO A., GUÉRIN S., and CHAMPION Y. Mechanical Behavior of
Zr-Based Bulk Metallic Glasses ..................................................................................................................... 167
SHANYAVSKII A. A. and POTAPENKO Yu. A. In-Service Fatigue Fracture Mechanisms in Covered
Disks of a TV3-117VK Helicopter Turbine Engine ....................................................................................... 171

Preface
This issue of the journal contains papers selected from contributions presented
during the 5th International Conference Materials Structure & Micromechanics of
Fracture (MSMF-5), Brno, Czech Republic, June 27–29, 2007.
The first conference of the MSMF series was held in Brno, June 1995. The
participants decided to repeat such conferences in Brno each three years. The basic idea
was to establish a periodical international forum presenting multiscale approaches in
fatigue and fracture of materials. Therefore, respective sections focused on atomistic
models, models based on crystal defects, numerical and statistical models based on
continuum mechanics, advanced experimental methods and relationships between
structure and mechanical properties appeared during the MSMF-2 conference in 1998. In
particular, the power of atomistic and mesoscopic approaches in fracture was clearly
demonstrated by participants at the MSMF-3 meeting in 2001. The view of multiscale
approaches in modeling deformation and fracture has created the framework of the
MSMF-4 conference in 2004.
The conference MSMF-5 has successfully curried on the tradition of previous
conferences. Nearly 180 scientists from 27 countries all over the world presented a variety
of fundamental relations between structural and mechanical characteristics of materials. In
collaboration with the International Advisory Board, the organizers asked Prof. V. Vitek
(University of Pennsylvania, USA), Prof. J. W. Morris (University of California, USA),
Prof. H. Mughrabi (University of Erlangen-Nurnberg, Germany), Dr. P. Lukas (Institute of
Physics of Materials, Academy of Sciences, Czech Republic), Prof. R. Pippan (Erich
Schmid Institute of Materials Science, Austria) and Prof. Y. Kondo (Kyushu University,
Japan) to prepare plenary key-note lectures. Additional top scientists were asked to give
key-notes in sections.
It is my pleasure to thank the editorial board of the journal for the readiness to
publish this volume devoted to MSMF-5. I would also like to thank all members of the
Organizing Committee, members of the International Advisory Board, session chairpersons
as well as many colleagues who helped in the preparation of the conference and,
particularly, in the preparation of the Proceedings.
Jaroslav Pokluda,
Guest Editor,
Chairman, MSMF-5
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 7

Scientific and Technical
Section
UDC 539. 4
Ab Initio DFT Study of Ideal Shear Strength of Polytypes of Silicon Carbide
Y. Umeno, 1,a Y. Kinoshita, 2,b and T. Kitamura 2,c
1 Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
2 Graduate School of Engineering, Kyoto University, Kyoto, Japan
a umeno@iis.u-tokyo.ac.jp, b yusuke-kinoshita@t02.mbox.media.kyoto-u.ac.jp,
c kitamura@me.kyoto-u.ac.jp
Ab initio density functional calculations are performed to investigate the ideal shear deformation of
SiC polytypes (3C, 2H, 4H, and 6H). The deformation of the cubic and the hexagonal polytypes in
small strain region can be well represented by the elastic properties of component Si4Ctetrahedrons.
The stacking pattern in the polytypes affects strain localization, which is correlated
with the generalized stacking fault (GSF) energy profile of each shuffle-set plane, and the ideal
shear strength. Compressive hydrostatic stress decreases the ideal shear strength, which is in
contrast with the behavior of metals.
Keywords: ideal strength, shear deformation, ab initio simulation, silicon carbide.
Introduction. Silicon carbide (SiC) possesses prominent properties such as high
mechanical strength, chemical stability and large band gap energy, and has been widely
used as thermal and mechanical functional material, electromagnetic functional material,
etc. Detailed investigations in atomistic and electronic level are required for SiC crystals
because they have a variety of polytype structures characterized by stacking sequence [1],
which contributes to their interesting mechanical properties. Thus, with the aim to
elucidate its mechanical deformation behavior, not only experimental studies but also
theoretical approach such as atomistic modeling have been carried out [2]. Ab initio (first
principles) calculations have also been performed [3–5] to give reliable theoretical
insights to the mechanical properties of SiC around the equilibrium state. However, the
investigations of the mechanical properties around highly strained conditions are
indispensable for understanding of deformation behavior of crystals. Although ab initio
investigations of the tensile properties of 3C(�)–SiC by Li and Wang [6] and of the shear
by Ogata et al. [7] have brought some interesting results, this issue deserves further
studies. In particular, it is important to theoretically evaluate the ultimate strength under
ideal shear deformation of polytypes, which is relevant to the critical shear stress at the
onset of dislocation nucleation from a pristine crystal, to understand the plasticity in the
atomistic scale. Moreover, the response of the ideal shear strength to compressive stresses
is worth investigating because local lattice configurations may receive shear deformation
in combination with normal stresses in experiments, namely nanoindentation.
Since the mechanical behavior at atomic scale is strongly correlated with the
electronic nature and it is difficult for empirical interatomic potentials to correctly
represent various properties away from the equilibrium state, it is important to study the
mechanical deformation by atomistic and electronic modeling, namely the ab initio
methodology.
© Y. UMENO, Y. KINOSHITA, T. KITAMURA, 2008
8 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Ab Initio DFT Study of Ideal Shear Strength ...
In this study, we perform ab initio calculations based on the density functional
theory (DFT) to investigate the ideal shear deformation of SiC polytypes (3C, 2H, 4H,
and 6H) with the aim to provide fundamental knowledge about the mechanical properties
of the crystals including their behavior under highly sheared strain conditions and the
ideal strength, focusing on the effect of the intrinsic polytype structure on the strain
localization and the ideal strength. We further explore the effect of hydrostatic pressure on
the ideal strength.
Structure of SiC Polytypes. SiC consists of tetrahedrons where vertices are
occupied by silicon atoms with carbons located in the center of gravity. The crystal
possesses various structures (SiC polytypes) with different stacking sequence, which are
denoted in Ramsdel’s notation as nX , where n is the number of layers along the c-axis
per periodic cycle and X is the identifier of crystal structure (C: Cubic and H:
Hexagonal). Figure 1 depicts the structures of 3C, 2H, 4H, and 6H polytypes. In this
study, shear deformation on the c-plane, which is (111) in cubic structure and (0001) in
hexagonal, is studied because it is associated with an important slip system of SiC. As is
schematically delineated in Fig. 2, cubic (3C) and hexagonal (2H, 4H, 6H, ...) crystals
have different symmetry in shear deformation due to the stacking structure [8]. Concerning
shear on the c-plane, 3C–SiC has three-fold symmetry resulting in different geometrical
configurations between shear deformations in and its opposite direction([ 121]). On the
other hand, hexagonal polytypes have six-fold symmetry in shear deformation on (0001)
plane because their stacking consists of Si4C-tetrahedrons facing opposite directions. The
shear deformations in a direction and its opposite (e.g., [ 0110] and [ 0110) ] are therefore
identical in hexagonal polytypes.
Fig. 1. Schematics of stacking sequence of SiC polytypes.
Simulation Procedure. We performed ab initio DFT calculations based on the
projector augmented wave (PAW) method within the framework of generalized gradient
approximation (GGA) using the Vienna Ab Initio Simulation Package VASP [9, 10]. The
plane-wave cutoff energy was set to 500 eV and the PW91-GGA functional [11] was
adopted.
In the setup the x, y, and z axes are in [ 0110]([ 121 ]), [ 2110]( 1 01), and
[0001]([111]), respectively. Shear deformation under zero and nonzero hydrostatic stress
is simulated as follows: After finding equilibrium lattice parameters of undeformed
crystals by energy minimization under the hydrostatic stress � h , shear deformation � zx is
applied to each simulation cell where atomic configuration are relaxed until all the forces
are below 0.005 eV/A and normal strains of the cell are adjusted so that normal stress
components are within �100 MPa from predetermined � h .
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 9

Y. Umeno, Y. Kinoshita, and T. Kitamura
Fig. 2. Schematics of symmetry in shear deformation of 3C and hexagonal SiC crystals.
Results and Discussion. Stress–Strain Relationship. Figure 3 shows stress–strain
relationships of the cubic and hexagonal polytypes (3C, 2H, 4H, and 6H) obtained by the
ab initio calculations. The curve of 3C differs from those of the hexagonal polytypes
because of the difference in the stacking structure, which is explained in more detail in
[8]. Although the stress-strain relations up to ��0.2 are almost identical between the
hexagonal polytypes, the polytype structure affects the deformation behavior at higher
strains and thus the ideal strength; the maximum stress of 2H is the highest and of 6H the
lowest. We find nontrivial effect of the structure of polytypes on the ideal strength � is ;
i.e., � is of 6H (29.83 GPa) is about 10% lower than that of 2H (32.97 GPa). This is
obviously due to the stacking pattern (structure) affecting the mechanical properties,
which will be discussed later on. The ideal strength of 3C–SiC obtained here, 30.3 GPa,
compares well with the value evaluated by the local density approximation (LDA) by
Ogata (29.5 GPa [12]).
Fig. 3. Stress–strain curves of SiC polytypes.
The ideal (theoretical) shear strength can be correlated with the critical shear
strength of dislocation nucleation in a pure crystal. For example, Bahr et al. [13]
demonstrated in their study of nanoindentation of tungsten and iron single crystals that the
maximum shear stress required for dislocation nucleation shows an excellent agreement
with the theoretical shear strength. Ohta et al. [14] devised a sophisticated experimental
procedure to evaluate the critical shear stress for dislocation nucleation in silicon, which
also compares well with the theoretical strength [15]. To the best or our knowledge, there
has been no experimental work extracting the critical shear stress for dislocation
nucleation in SiC, but we believe that the value we obtained in this study must be a good
prediction. Experimental evaluation of the critical shear stress for dislocation nucleation
in SiC is highly desirable although it can be demanding due to the requirement of special
techniques such as preparation of specimens with an ideal shape.
10 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Ab Initio DFT Study of Ideal Shear Strength ...
Normal Strains and Volume. Changes in normal strains and volume of the SiC
polytypes during shear deformation are presented in Fig. 4. The hexagonal polytypes
show nearly the same evolution of normal strains with increasing shear strain. In SiC(3C)
the evolution of normal strains is different and changes in �xx and � yy are more obvious
than in the hexagonal polytypes; the former decreases and the latter increases as the shear
strain grows. Relative volume, VV0�( 1��xx )( 1��yy )( 1��zz),
however, changes
similarly both in 3C and the hexagonal polytypes; i.e., the volume decreases with
increasing shear strain.
a b
Fig. 4. Changes in normal strains (a) and volume during shear of SiC polytypes (b).
Strain Localization. To investigate the deformation of each Si4C -tetrahedron lattice,
we now show in Fig. 5a the “bond shear strain,” � b , representing deformation of each
atomic bond as in the schematic. In the hexagonal polytypes � b differs depending on the
layer, signifying that bonds of specific layers deform more than the others. This is
analogous to non-uniform deformation or strain localization in inhomogeneous materials
(structure). Unlike 3C, inhomogeneous stacking structure intrinsically existing in the
hexagonal polytypes causes the strain localization, which affects the ideal strength.
The strain localization shows deviation from the intuitive picture of the deformation
that lattices A, B, and C are ‘softer’ and A �,
B �,
and C� are ‘stiffer’. In 6H–SiC, while
lattices A and B accommodate large and almost identical bond shear strain, lattice C shows
a small deformation and its bond shear strain is even smaller than that of C �.
This implies
that the deformability of the bond is affected by the stacking discontinuity between
lattices C and B � ( C� and A); i.e., lattice C is stiffened by the overlaying lattice B � (and
similarly, C� is softened by A). This effect is seen in the other hexagonal polytypes as well.
The difference in deformation among the layers can be explained by the generalized
stacking fault (GSF) energy of the shuffle-set layers shown in Fig. 5b. Here, the lattice
over a shuffle-set plane is rigidly shifted along the x direction without atomic relaxation
while the lattice below is fixed, and the energy increase as a function of the rigid shift is
evaluated (see the schematic in the figure).
The profile of GSF energy depends on the layer, meaning that the bond in each layer
has different “deformability.” The layer showing lower peak in 0�xs�1 has a higher
deformability, which corresponds to strain localization found in Fig. 5a. The GSF energy
profile supports the above-mentioned hypothesis of the mechanism that the deformability
of the bond in question is affected by the stacking discontinuity. The GSF energy
landscape can be a profile representing the deformability of each bond subject to shear
although it does not incorporate the effect of atomistic relaxation.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 11

Y. Umeno, Y. Kinoshita, and T. Kitamura
a
Fig. 5. (a) Evolution of bond shear strain, � b . A, B, C and those with a prime denote the
tetrahedrons as depicted in Fig. 1. (b) GSF energy landscape of 2H and 4H with a shuffle set being
rigidly shifted along the x direction. The abscissa is the shift displacement normalized with respect
to the lattice width, xs� xdX. Effect of Pressure. Figure 6 compares the ideal shear strengths of the polytypes
under zero and nonzero hydrostatic compression. In the figure, both the abscissa and the
0
ordinate are normalized by � is,
the ideal shear strength under no compression.
Hydrostatic compression significantly decreases the ideal strength in all the hexagonal
polytypes studied here. The response of the ideal shear strength to compression can be
explained by the volume change during shear; i.e., the systems contract as the shear strain
grows and the compressive normal stress helps the shear deformation. This phenomenon
is in contrast with the properties of metals, where, in general, the ideal shear strength
increases under compressive pressure [16, 17].
Fig. 6. Ideal shear strength as a function hydrostatic stress. Both abscissa and ordinate are
0
normalized by �is (the ideal shear strength at �h � 0).
12 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
b

Ab Initio DFT Study of Ideal Shear Strength ...
It was demonstrated by Krenn et al. [18] that the effect of compressive stress to the
shear strength is important in the interpretation of the critical stress for plastic deformation
found in nanoindentation experiments, because the contribution of normal stress
components can change the ideal strength in shear. Therefore, our finding here is crucial
as it shows that the effect of compressive stress to the shear strength of covalent system
can be different even qualitatively from that of metals. As it has been pointed out, the
relation between shear and normal stresses exhibits a strong anisotropic character [16] and
dependence on atom species [17]. Further extensive studies for various crystals and stress
conditions will be necessary to elucidate its mechanism.
Conclusions. We have investigated the ideal shear deformation of SiC polytypes
(3C, 2H, 4H and 6H) by means of ab initio DFT calculations based on the generalized
gradient approximation. The variety of the stacking pattern in the polytypes causes strain
localization, which is correlated with the GSF energy profile of each shuffle-set plane, and
difference in the ideal shear strength. We also examined the effect of hydrostatic
compression to the shear deformation to reveal that the compressive stress decreases the
ideal shear strength in all the polytypes studied here, which is in contrast to metals, where
in general the ideal shear strength is increased by compression. More extensive studies
will be required to elucidate the mechanism of the effect of the normal stress because it
can be highly anisotropic and susceptible to the interatomic bonds of the atom species
Acknowledgments. One of the authors (Y.U.) acknowledges financial support from the Grant-in-Aid
for Scientific Research of Japan Society of the Promotion of Science (JSPS, No. 1876008).
1. P. T. B. Shaffer, Acta Cryst. B, 25, 477 (1969).
2. W. J. Choyke, H. Matsunami, and G. Pensl, Silicon Carbide, Akademie Verlag, Berlin (1997).
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3685 (1991).
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8. Y. Umeno, Y. Kinoshita, and T. Kitamura, Model. Simul. Mater. Sci. Eng., 15, 27 (2007).
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Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 13

UDC 539. 4
Crack Initiation and Endurance Limit of Hard Steels under Multiaxial
Cyclic Loads
H. Bomas, 1,a R. Kienzler, 2 S. Kunow, 3 G. Loewisch, 4 and R. Schroeder 2
1 Stiftung Institut für Werkstofftechnik, Bremen, Germany
2 University of Bremen, Bremen, Germany
3 Edelstahlwerke Südwestfalen, Siegen, Germany
4 Universität der Bundeswehr, Neubiberg, Germany
a bomas@iwt-bremen.de
The endurance limit and the mechanisms of fatigue crack initiation in the high cycle regime were
investigated using round specimens of the bearing steel 52100 under longitudinal forces and
torsional moments and combinations of these loads. Three specimen types were examined: smooth
specimens and specimens with circumferential notches with radii of 1.0 and 0.2 mm. The influence
of mean and multiaxial stresses on the endurance limit can be understood by consideration of crack
initiation mechanisms and micro-mechanics. Crack initiation took place at oxides, carbonitrides
and at the surface. The mechanisms of crack initiation could be related to the load type: Loads with
rotating principal stresses are more damaging for nitrides than for oxides. Increasing maximum
stresses are more dangerous for nitrides than for oxides, and introduce more damage to the surface
than to the nitrides. Normal stresses are more damaging for oxides than shear stresses. The
endurance limits were calculated by means of an extended weakest-link model which combines
volume and surface crack initiation with related fatigue criteria. For volume crack initiation the
criterion of Dang Van was used. For the correct description of the competing surface crack
initiation, a new criterion was applied. With this concept, a prediction of the endurance limit is
possible for loads which produce critical planes and range within a limited regime of stress ratios.
Keywords: endurance limit, bearing steel, crack initiation, multiaxial load, weakest-link
model, fatigue criterion.
Introduction. This paper describes a calculation method for hard steels which
allows the prediction of the endurance limit of parts of arbitrary geometry based on data
that have been gained from tests on a set of reference specimens under certain load
conditions. For the development of this calculation method, the endurance limits of
smooth and notched specimens under tension-compression, repeated tension, alternating
torsion and different superpositions of cyclic tensile and torsional loads have been
determined experimentally. Hereby, the influence of mean stresses, multiaxial stress
conditions and stress gradients on the fatigue behavior could be evaluated. Based on the
collected data, a calculation method was applied which is based on the weakest-link
model [1] and on suitable high-cycle fatigue criteria for surface and volume crack
initiation [2, 3].
Material and Specimens. The experiments were carried out on the bearing steel
SAE 52100 remelted under vacuum. From this material, smooth and notched specimens
were turned with a net diameter of d � 6 mm (Fig. 1). After turning, the specimens were
heat treated as follows: 855�C, 25 min/salt melt 220�C, 6 h/washing 65�C. In this bainitic
condition the material had a hardness of 715 HV 10 and the following tensile properties:
Rm � 2467 MPa, R p02 . 2115 � MPa, and E � 202 GPa. Finally, the specimens were
ground in the gauge region, which resulted in the following residual stresses at the surface
of the smooth specimens: �479 MPa in the longitudinal direction and �384 MPa in the
tangential direction.
© H. BOMAS, R. KIENZLER, S. KUNOW, G. LOEWISCH, R. SCHROEDER, 2008
14 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Crack Initiation and Endurance Limit of Hard Steels ...
Fig. 1. Geometry of the fatigue specimens in the gauge region.
Fig. 2. Loading of a notched specimen and relevant coordinates at the notch root surface, x =
coordinate parallel to the rotation axis, y = tangential coordinate.
Endurance Limits. The specimens were cycled in a testing system that allows the
superposition of longitudinal and torsional loads (Fig. 2). The applied loads can be
described with a mean longitudinal load Fm , a corresponding amplitude Fa , and an
amplitude M a of the torsional moment. Longitudinal load and torsional moment were
cycled with the same frequency f and combined in phase or with a phase shift ��� 2.
The resulting surface load stress tensor at the notch root has the following form:
��x
��m��a sin( 2�ft ) �xy ��a sin( 2�ft��) 0�
�
�
� �yx ��asin( 2�ft��) 0 0�.
�
�
� 0 0 0�
The endurance limits under different load types were determined by constant
amplitude tests at different amplitudes. Endurance of a specimen was defined as reaching
10 7 cycles without failure. The endurance limits were assumed to obey a two-parametric
Weibull distribution:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 15
(1)

H. Bomas, R. Kienzler, S. Kunow, et al.
( S S )
F( Sa) � � ,
�
( T T )
1 2 FT ( a ) � � .
�
1 2 (2)
a D m
a D m
Table 1 gives a survey over the tested variants and the measured endurance limits.
Table 1
Experimental Variants and Corresponding Endurance Limits
Variant S a R S T a � Notch radius
[mm]
Endurance limit
[MPa]
m Symbol
in Fig. 4
1 Sa �1 0 � 866 20 �
2 Sa �1 0 1.0 631 23 �
3 Sa �1 0 0.2 373 9 �
4 Sa 0.1 0 � 502 21 �
5 Sa 0.4 0 � 437 48 �
6 Sa 0.5 0 � 419 51 �
7 Sa 0.6 0 � 371 33 �
8 0 Ta � 540 55 �
9 0 Ta 1.0 539 16 �
10 0 Ta 0.2 334 20 �
11 Sa �1 0.5Sa 0 � 734 19 �
12 Sa �1 0.5Sa 0 1.0 520 14 �
13 Sa �1 0.5Sa 0 0.2 345 13 �
14 Sa �1 0.5Sa � 2 � 607 45 �
15 Sa �1 0.5Sa � 2 1.0 406 25 �
16 Sa �1 0.5Sa � 2 0.2 283 6 �
17 Sa �1 Sa � 2 � 431 11 �
18 Sa 0.1 0.5Sa � 2 � 417 31 �
19 Sa �1 Sa 0 � 477 7 �
Fatigue Crack Initiation. Three types of crack initiation were observed: crack
initiation at the surface, at aluminum oxides and in titanium carbonitrides. The latter two
types are shown in Fig. 3. Crack initiation at aluminum oxides is due to matrix failure,
since the inclusion is not bonded to the matrix und thus concentrates the stress in the
surrounding matrix. Crack initiation in titanium carbonitrides is due to failure of the
inclusion itself, since the inclusion is well bonded to the matrix and concentrates the stress
in itself. The cracks exhibit cleavage of the inclusion in well defined crystal planes. All
notched specimens exhibited crack initiation at the surface which is due to the stress
gradient.
Table 2 shows the crack initiation sites in smooth specimens. Several tendencies can
be observed: Under tensile loads starting from a stress ratio R ��1, the titanium
carbonitrides get more involved in crack initiation as the stress ratio increases to R � 0.1.
Further increase of the stress ratio leads to more frequent crack initiation at the surface.
Torsional loads are obviously most dangerous for the surface. A comparison of proportional
loading and non-proportional loading shows that the titanium carbonitrides are mostly
damaged by non-proportional loading.
16 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Table 2
Crack Initiation and Endurance Limit of Hard Steels ...
Observed Crack Initiation Sites in Smooth Specimens
Variant S a R S T a � Crack initiation at S S
a � 90
1 Sa �1 0 33% aluminum oxide
45% titanium carbonitride
22% unknown
4 Sa 0.1 0 100% titanium carbonitride
5 Sa 0.4 0 77% titanium carbonitride
23% surface
6 Sa 0.5 0 11% aluminum oxide
33% titanium carbonitride
56% surface
7 Sa 0.6 0 29% titanium carbonitride
71% surface
8 0 Ta 100% surface
11 Sa �1 0.5Sa 0� 63% aluminum oxide
32% titanium carbonitride
5% surface
14 Sa �1 0.5Sa 90� 67% titanium carbonitride
8% surface
25% unknown
a b
Fig. 3. Crack initiation at an aluminum oxide (a) and at a titanium carbonitride (b).
Calculation of Endurance Limits. The endurance limits were calculated on the
basis of the weakest-link concept, as described before [2]. For crack initiation in the
volume Dang Van’s criterion [3] was applied, which uses the equivalent value � a,max� �V p max . For crack initiation at the surface a criterion of Bomas, Linkewitz, and Mayr [2]
was applied, which uses the equivalent value �a,max ��A pm.
The model parameters
shown in Table 3 were determined by taking the variants 1, 2, 4, 8, and 9 as references.
Figure 4 shows the calculated and the measured endurance limits as nominal stress
amplitudes S a or Ta . Most endurance limits are well calculated. Large differences
between experiment and calculation are exhibited by the variants 5, 6, 7, 14, and 15.
The variants 5, 6, and 7 exhibit high stress ratios of R � 0.4, 0.5, and 0.6,
respectively. If the endurance limits of these variants are drawn in the Haigh diagram with
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 17

H. Bomas, R. Kienzler, S. Kunow, et al.
the values of the variants 1 and 4, it can be seen that there is a non-linear relation between
endurance limit and mean stress. This is typical for hard steels, e.g., [4], but is not
described by the applied fatigue criteria.
Table 3
Model Parameters for Calculation of the Endurance Limits
Reference area or volume � W 0 , MPa � m
2
Surface A A0 � 213 mm 551 1.32 10
Volume V 3
V0 �192 mm 629 0.59 14
Fig. 4. Predicted and measured nominal endurance limits, expressed as nominal longitudinal stress
S a or nominal torsional stress T a .
Fig. 5. Surface shear stress amplitudes in a specimen of variant 14 normalised with the normal stress
amplitude in x-direction (0� � �180�, 0� � � 360�).
An explanation of the cartesian coordinates
is given in Fig. 2.
18 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Crack Initiation and Endurance Limit of Hard Steels ...
The variants 14 and 15 are phase-shifted superpositions of tension and torsion.
Variant 14 is very special, because it has no critical plane. Figure 5 shows the shear stress
amplitudes in the cutting surface planes normalised with the normal stress amplitude in
x-direction. � and � indicate the direction of vector normal to the plane. Since many
planes see the maximum shear stress amplitude, the damage of the load is underestimated
by the applied fatigue criteria. Especially the titanium carbonitrides seem to be victims of
the multi-plane damage, since they fail by cleavage fracture in crystal planes. The
specimens of variant 15 have a mild notch, and the stress situation is similar to that of
variant 14. The specimens of variant 16 have a sharp notch, and due to the dominance of
the stress concentration factor for tension, the stress situation in the notch root is more
similar to that of variant 3. It can be seen in Fig. 4 that the endurance limits of these
variants are very similar, which applies for the experimental values as well as for the
calculated ones.
Conclusions. In this work, the influence of notches, stress gradients, mean stresses
and multiaxial loads on the endurance limit of ground specimens made of the bearing steel
SAE 52100 in a bainitic condition was investigated. The influence of notches and of stress
gradients can be described by application of a weakest-link concept. A prediction of the
endurance limit is possible for loads with �� 1 R �01
. which produce critical planes. The
crack initiation in smooth specimens is very much influenced by the load type. Three
crack initiation sites were observed: oxides, carbonitrides and surface. Loads that produce
more than one critical plane lead to further damage of the titanium carbonitrides. Under
push-pull or repeated-pull condition the maximum stress is relevant for crack initiation:
With increasing maximum stress, at first titanium carbonitrides and after that the surface
get more and more involved in crack initiation.
1. W. Weibull, “A statistical theory for the strength of materials,” Royal Swed. Inst. Eng. Res.,
151 (1939).
2. H. Bomas, T. Linkewitz, and P. Mayr, Fatigue Fract. Eng. Mater. Struct., 22, 733 (1999).
3. K. Dang Van, B. Griveau, and O. Message, in: M. W. Brown and K. J. Miller (Eds.), Biaxial
and Multiaxial Fatigue (EGF 3), Mechanical Engineering Publications (1989), p. 479.
4. E. Haibach, Betriebsfestigkeit, Springer (2002).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 19

UDC 539. 4
Elastic Properties of B19’ Structure of NiTi Alloy under Uniaxial and
Hydrostatic Loading from First Principles
P. Šesták, 1,a M. Èerný, 1,b and J. Pokluda 1,c
1
Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of
Technology, Brno, Czech Republic
a sestak@kn.vutbr.cz, b cerny.m@fme.vutbr.cz, c pokluda@fme.vutbr.cz
The uniaxial and hydrostatic deformations of martensitic structure B19’ of NiTi shape memory alloy
are studied using first-principles calculations. The bulk and Young’s moduli and the theoretical
strength under uniaxial tension and hydrostatic loading are computed from crystal response to
applied deformations. The behavior of angle � of the B19’ structure was investigated along the
whole deformation path. The computed values of Young’s moduli are compared with available
experimental results. The results obtained complement and extend the already known
characteristics of NiTi alloy.
Keywords: NiTi, B19’, shape memory alloy, first principles, ab-initio, elastic properties,
theoretical strength, uniaxial and hydrostatic deformation.
Introduction. The shape memory alloys (SMA) are important materials for many
industrial as well as medical applications owing to their shape memory effect. This effect
is connected with a transformation between martensitic and austenitic structure, which can
be started by an external pressure or temperature. There are several types of the
transformations, depending on a particular alloy.
The nickel-titanium alloy is one of the most important types of SMA. It is widely
used in medicine (stents, bone implants, etc.). The NiTi alloy can transform from the
monoclinic B19’ (martensitic) to cubic B2 (austenitic) structure and vice versa. An
extensive overview of a current state of the art can be found in the paper by Otsuka and
Ren [1].
The aim of this work is to compute the Young E and bulk B moduli and the
theoretical strengths under uniaxial and hydrostatic (isotropic) loading. The Young
modulus has been computed for three crystallographic directions (E [100], E [010], and
E [001]) parallel to primitive translation vectors (r 1 , r 2 , and r 3 ) shown in Fig. 1. The
dependence of the � angle (between r 1 and r 3 vectors) on the applied uniaxial
deformation has been also investigated.
Fig. 1. The martensitic structure (B19’) of NiTi alloy with marked crystallographic directions.
©P.ŠESTÁK, M. ÈERNÝ, J. POKLUDA, 2008
20 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Electronic Structure Computations. All quantities of interest are computed from
the total energy Etotal of the system at hand as a function of an appropriate deformation
and from the Hellman–Feynman stress tensor.
The total energies and stresses were computed by the Abinit program code. Abinit is
a great tool for electronic structure calculations developed by the team of Prof. Xavier
Gonze at the Université Catholique de Louvain [2, 3], which is distributed under the GNU
General Public License. Another additional package including pseudo-potentials [4]
together with its generators, manuals, tutorials, examples, etc. is available at [5].
The calculations were performed using GGA norm-conserving pseudo-potentials and
the cutoff energy was set to 1000 eV for computations of elastic moduli and 800 eV for
theoretical strength evaluation. The solution was considered to be self-consistent when the
energy difference of three consequent iterations became smaller than 0.1 �eV for
computation of elastic properties and 1.0 �eV for the theoretical strength.
During the uniaxial deformation the structure must be relaxed in order to allow the
Poisson contraction. The relaxations were made by an external procedure utilizing the
Hellman-Feynman stress tensor [6] computed by the Abinit code.
Computation of Elastic Moduli and Theoretical Strength. The Young’s modulus
can be computed as
d Etotal
E �
V d
1
2
, (1)
2
�
0
where � is the relative uniaxial deformation, �� aa0�1. Similarly, the uniaxial stress
can be evaluated as
uni
� �
V
dEtotal
d�
1
. (2)
0
The bulk modulus and the hydrostatic stress were calculated according to the
relations
B �
V
d Etotal
dv
1
0
2
2
(3)
and
hyd
� �
V
dEtotal
dv
1
, (4)
0
Elastic Properties of B19’ Structure of NiTi Alloy ...
where v is the relative volume v�V0V�1. Both stresses approach their maxima at the
points of inflection of Etotal ( �) or Etotal ( v)
dependences. If no other instability appears
before reaching the points, their maximum values specify the corresponding theoretical
strength values � id .
Results. The experimental and ab-initio values of primitive translation vectors and �
angle of the B19’ structure are displayed in Table 1. The ab-initio results predict slightly
larger values than those found in experiment. This overestimating of translation vectors is
a typical effect of GGA pseudopotential type but the related errors are smaller than 5%.
Table 2 contains the computed values of the Young’s and bulk moduli of the
martensitic B19’ and austenitic B2 structures. As can be seen, the Young’s moduli of B19’
are higher than those of the austenitic B2 structure for all the directions studied. These
results are in contrast with experimental and finite element method (FEM) values, which
predict the Young’s modulus of martensite to about one-third to one-half of that of
austenite [7].
This can be explained by the fact that the experimental data were measured on
polycrystalline samples at finite temperatures, whereas the atomistic model does not allow
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 21

P. Šesták, M. Èerný, and J. Pokluda
for any shear deformation of martensite variants, and describes a homogeneous deformation
of a single crystal at the absolute zero temperature. On the other hand, the bulk modulus
for the B19’ structure is lower than that for the B2 structure. Table 3 contains values of the
theoretical strength for all applied deformations.
Table 1
The Experimental [1] and Ab-Initio Crystallographic Data for B19’ Structure
Parameter Experimental Ab initio
a0 , Å 2.889 3.007
b0 , Å 4.120 4.121
c0 , Å 4.622 4.813
�, deg 96.8 100.6
V , Å 3
54.63 58.61
Table 2
The Elastic Moduli of the B19’ and B2 Structures, as Obtained
from Present Ab-Initio Calculations along with Experimental [7] Results
Structure\moduli E [100], GPa E [010], GPa E [001], GPa B, GPa
B19’ (ab-initio)
B2 (ab-initio)
B2 (FEM)
96
72
69
124
72
69
Under an applied deformation, the angle � changes as a result of the relaxation
procedure. The dependence of the � angle on the applied deformation is shown in Fig. 2.
126
72
69
137
155
–
Table 3
Computed Values of the Theoretical Strength of the B19’ and B2 Structures
Structure\theoretical
strength
uni uni uni hyd
�id [100], GPa �id [010], GPa �id [001], GPa �id , GPa
B19’ (ab-initio) 19.0 27.5 20.7 22.1
B2 (ab-initio) – – – 24.0
Fig. 2. The angle � as a function of applied deformation. The detail of the range close to the
nondeformed state is depicted at the bottom right.
22 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Elastic Properties of B19’ Structure of NiTi Alloy ...
The points related to the theoretical strength are also marked (the inflection point in the
dependence Etotal ( �) resp. Etotal ( v)
by dashed vertical lines. One can see that the angle
� grows for all the deformation paths except for the [010] direction. Note that the [010]
direction is perpendicular to vectors r1 and r3 ; therefore, the decrease in the � angle
during the [010] deformation is to be expected.
Conclusions. The uniaxial and hydrostatic deformation of martensitic structure B19’
of NiTi shape memory alloy was studied using first-principles calculations. The results of
computations of Young’s and bulk moduli are as follows: E [100] � 96 GPa, E [010] �
124 GPa, E [001] � 126 GPa, and B � 137 GPa. During the uniaxial and hydrostatic
deformation the theoretical strengths were computed for all cases of applied deformations:
uni uni uni hyd
� id [100] � 19.0 GPa, � id [010] � 27.5 GPa, � id [001] � 20.7 GPa, and � id �
22.1 GPa. The Young moduli of B19’ are higher than those of the austenitic B2 structure
for all the directions studied and the bulk modulus for the B19’ structure is lower than that
for the B2 structure. The angle � grows for all deformation paths except for the [010]
direction.
Acknowledgments. This research was supported by research projects GA 106/05/H008 and
MSM 0021630518.
1. K. Otsuka and X. Ren, Prog. Mater. Sci., 50, 511 (2005).
2. X. Gonze, J.-M. Beuken, R. Caracas, et al., Comp. Mater. Sci., 25, 478 (2002).
3. X. Gonze, G.-M. Rignanese, M. Verstraete, et al., Zeit. Kristallogr., 220, 558 (2005).
4. M. Fuchs and M. Scheffler, Comp. Phys. Communicat., 119, 67 (1999).
5. http://www.abinit.org
6. D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B, 71 (2005).
7. X. M. Wang and Z. F. Yue, Comp. Mater. Sci., 39, 697 (2007).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 23

UDC 539. 4
Creep-Induced Structural Changes in Ni–Si–B Amorphous Alloy
A. Juríková, 1,a J. Miškuf, 1,b K. Csach, 1,c and V. Ocelík 2,d
1 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
2 Department of Applied Physics, Materials Science Centre and Netherlands Institute of Metals
Research, University of Groningen, Groningen, The Netherlands
a akasard@saske.sk, b miskuf@saske.sk, c csach@saske.sk, d v.ocelik@rug.nl
The influence of the stress annealing on the reversible structural relaxation of a Ni–Si–B
amorphous ribbon was studied. Creep-induced structural changes in the amorphous structure were
derived from anisothermal DSC and dilatometric experiments. It is demonstrated that considerable
enthalpy and specimen length variations associated with the reversible structural relaxation are
observed after previous creep at higher temperatures.
Keywords: structural relaxation, inelastic strain, Ni-based amorphous alloys.
Introduction. Metallic glasses represent a class of metallic materials with unique
physical and mechanical properties. From a thermodynamic point of view they are
unstable and annealing them at elevated temperatures leads to structural relaxation. Many
papers dedicated to structural changes, which manifest themselves through changes in
various physical properties, have been published up to now [1–4]. They show that besides
irreversible structural relaxation accompanied by annealing-out and quenching-in effects
below the glass transition temperature, there are reversible structural changes brought
about by thermal, magnetic, or mechanical effects. Atomic disorder and defects of various
levels also play an important role in magnetic properties of metallic glasses [5, 6].
Glassy alloys with a high Ni content were found to exhibit a glass transition before
crystallization. The combination of high glass-forming ability and good mechanical and
soft magnetic properties of the Ni–based glassy alloys indicates their perspective
applications [7]. The homogeneous deformation ability is influenced by the structure of
amorphous alloys, namely by the amount and mobility of defects. Creep and creep
recovery experiments can help understanding these phenomena [8]. For this purpose,
creep-induced structural changes in the Ni–Si–B amorphous alloy were studied by means
of differential scanning calorimetry (DSC) and thermomechanical analysis (TMA)
methods. The aim of the present work is to find out how the creep applied at different
temperatures influences the reversible structural relaxation of the Ni-rich amorphous
alloy.
Experimental Details. An amorphous metallic ribbon of the nominal composition
Ni77.5Si7.5B15 (at.%) with a thickness of 18.8 �m prepared at the Institute of Physics of the
Slovak Academy of Sciences in Bratislava by rapid quenching of the melt on a rotating
disc was used in experiments. The amorphous structure of the samples was checked by
X-ray diffraction. The crystallization temperature of the amorphous ribbon determined by
differential scanning calorimetry for an as-quenched sample at the temperature of the first
crystallization peak onset was Tx �492�C. The specimens of 5 mm width were cut from as-received ribbon and initially heated
up to a preannealing temperature of 380�C and kept for 30 min to eliminate further
irreversible structural relaxation processes. After cooling down, they were annealed at
temperatures of 300, 325, and 350�C for about 18 hours under an external tensile stress of
282 MPa. After finishing the stress-annealing, the samples were cooled down to room
temperature and then unloaded. Some preannealed samples were not subjected to loading
and were used as reference specimens. Heat treatments were performed in a tube furnace
©A.JURÍKOVÁ, J.MIŠKUF, K. CSACH, V. OCELÍK, 2008
24 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Creep-Induced Structural Changes in Ni–Si–B Amorphous Alloy
in nitrogen atmosphere. DSC measurements were carried out using a Perkin Elmer DSC 7
differential scanning calorimeter. The enthalpy changes were measured under linear
heating with a constant heating rate of 20�C/min for both the stress-annealed and the
reference samples.
An additional type of experiment was carried out by means of a Setaram TMA 92
thermomechanical analyzer in the tension arrangement with an absolute resolution of 10
nm and temperature stability better than 0.2�C. A flow of pure nitrogen was used to
protect a sample. The same sample with an initial length of 15 mm underwent several
thermal treatments. The initial structure was stabilized by two subsequent heatings to the
temperature 400�C that lies below the glass transition temperature of this amorphous
material. Such a thermally treated sample was considered as a reference one. After creep
annealing and cooling down to room temperature, the length changes under linear heating
with a rate of 10�C/min were recorded. Creep annealing was performed at temperatures of
195, 345, and 370�C for 18 hours under the applied mechanical stress 100 MPa.
Results and Discussion. Typical DSC traces recorded for samples annealed for a
long time under the applied stress and without it at a temperature of 325�C are shown in
Fig. 1. The insert shows a DSC thermogram for the whole measured temperature range.
The arrows marked T g and T x indicate the glass transition and crystallization onset
temperatures, respectively. Only the part of the DSC thermogram in the temperature range
up to the glass transition temperature was taken into account.
Fig. 1. DSC traces recorded for the samples annealed at 325�C under and without stress. The insert
shows a DSC thermogram for the whole measured temperature range.
The DSC traces obtained for samples subjected to stress annealing and for the
load-free annealed samples (reference ones) have a similar shape. This trend was observed
for all the stress annealing temperatures. The DSC scans recorded for the stress-annealed
samples were always found to lie below those for the reference samples. This means that
the structure of the samples subjected to loading is more packed according to the
directional structural relaxation model [9] that estimates the influence of the mechanical
stress on the structural relaxation of the samples. The extent of this phenomenon increases
with increasing annealing temperature.
Figure 2 shows the differences of measured DSC data between the samples annealed
at indicated temperatures under and without stress. It can be seen that the difference is the
larger, the higher the stress annealing temperature. However, the stress annealing at higher
temperatures leads above all to a dramatic increase in the relative amount of lower
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 25

A. Juríková, J.Miškuf, K. Csach, and V. Ocelík
activation energy processes. Defects with a lower activation energy are especially
responsible for reversible structural relaxation [10, 11].
To estimate the influence of creep conditions on the structure relaxation processes,
some additional thermomechanical experiments were carried out. A sample was subjected
to annealing at different temperatures under an applied load of 100 MPa for about 18 hours.
This resulted in the total strains derived from dilatometric experiments as summarized in
Table 1.
Table 1
Total Creep-Induced and Recovered Strains Derived from Dilatometric Experiments
Creep temperature
[�C]
195
345
370
Creep strain Recovered strain
[%]
[�m] [%]
4.67
56.75
108.15
0.03
0.38
0.72
0.02
0.10
0.08
Fig. 2. The difference between the DSC traces recorded for the samples annealed at indicated
temperatures under and without stress.
The higher temperature of creep annealing was applied, the higher total deformation
was observed. Maximum permanent strain of 0.72% was introduced during creep
annealing at a temperature of 370�C.
After the creep annealing, thermal expansion curves were measured during linear
heating. The thermal expansion was accompanied by relative contraction due to creep
recovery processes. Nearly periodic alternations on dilatometric curves were caused by
small non-linearity of the heating rate due to the temperature controller setting. The creep
recovery contributions to the length changes under linear heating were estimated by
subtracting the elongation curve values of the reference sample from those obtained after
creep annealing at chosen temperatures.
Figure 3 shows the temperature dependence of creep recovery contributions to the
length changes under linear heating after creep annealing realized at indicated temperatures.
At higher temperatures, the amount of the recovered inelastic strain increases up to the
maximum value of 0.1% in the case of annealing deformation defects introduced during
creep applied at a temperature of 345�C (Table 1). Subsequent increasing of the creep
26 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Creep-Induced Structural Changes in Ni–Si–B Amorphous Alloy
Fig. 3. The temperature dependence of the recovered inelastic strain measured after a long-time
creep annealing at indicated temperatures.
annealing temperature has only a small influence on the measured value of the total creep
recovery strain . A decreased sensitivity of the recovered strain value to the creep-induced
one at higher temperatures can be caused by a relatively high heating rate used in the
dilatometric experiments. At higher heating rates and given temperatures, the creep
recovery processes caused by higher activation energy defects cannot be fully activated.
Conclusions. Accumulation of the creep strain of the Ni–Si–B amorphous ribbon is
associated with structural changes observed as heat flow evolution under linear heating
during the DSC experiment. An increase in the creep-induced strain leads to a larger
amount of recovered inelastic strain, but only to a certain extent. At higher temperatures
and higher values of the creep-induced strain, the relative amount of the recovered
inelastic strain does not increase.
Acknowledgment. This work was supported by the Slovak Grant Agency for Science –
VEGA.
1. A. Böhönyey, G. Huhn, L. F. Kiss, et al., Mat. Sci. Eng. A, Suppl., Proc. of the 9th Int. Conf.
on Rapidly Quenched & Metastable Materials (1997), p. 154.
2. K. Russew and F. Sommer, J. Non-Cryst. Solids, 319, 289 (2003).
3. K. Pêkala, P. Jaœkiewicz, and D. Oleszak, Mat. Sci. Eng. A, Suppl., Proc. of the 9th Int. Conf.
on Rapidly Quenched & Metastable Materials (1997), p. 121
4. E. Jakubczyk and M. Jakubczyk, Czech. J. Phys., 54, D165 (2004).
5. A. Kaleziæ-Glišoviæ, L. Novakoviæ, A. Marièiæ, et al., Mat. Sci. Eng. B, 131, 45 (2006).
6. A. Lovas, K. Bán, J. Kováè, et al., Czech. J. Phys., 54, D89 (2004).
7. B. Shen and A. Inoue, Mater. Trans., 44, No. 7, 1425 (2003).
8. K. Csach, V. Ocelík, J. Miškuf, et al., IEEE Trans. Magn., 30, No. 2, 496 (1994).
9. V. A. Khonik, Phys. Stat. Sol. (a), 177, 173 (2000).
10. A. Juríková, K. Csach, J. Miškuf, et al., Centr. Eur. J. Physics, 5, No. 2, 177 (2007).
11. V. Ocelík, K. Csach, A. Kasardová, et al., Mat. Sci. Eng. A, 226-228, 851 (1997).
Received 28. 06. 2007
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UDC 539. 4
Failure of Zr50Ti16.5Cu15Ni18.5 Amorphous Metallic Ribbon
J. Miškuf, 1,a K. Csach, 1,b A. Juríková, 1,c V. Ocelík, 2,d V. Bengus, 3,e
and E. Tabachnikova 3,f
1 Institute of Experimental Physics, Slovakia Academy of Sciences, Kosice, Slovakia
2 Department of Applied Physics, Materials Science Centre and Netherlands Institute of Metals
Research, University of Groningen, Groningen, The Netherlands
3 Verkin Institute for Low Temperature Physics & Eng. UAS, Kharkov, Ukraine
a miskuf@saske.sk, b csach@saske.sk, c akasard@saske.sk, d v.ocelik@rug.nl,
e bengus@ilt.kharkov.ua, f tabachnikova@ilt.kharkov.ua
The deformation and fracture behavior of Zr50Ti16.5Cu15Ni18.5 bulk amorphous metal in the form of a
thin ribbon have been determined in tensile test at room temperature. The fracture is localized in a
major shear band and the fracture angle between the tensile stress axis and the fracture plane is
close to 45�. Fractographic observations have revealed that the fracture surface of the amorphous
metallic glass consists mainly of a vein-like pattern morphology. We present a scheme of three
zones of fracture surface morphology: progressive smooth sliding region (A), dominating vein like
pattern (B), and river-like ripples (C).
Keywords: fracture, bulk amorphous alloy, vein-like pattern.
Introduction. Amorphous metallic alloys in the form of ribbons with thickness less
than 50 �m are prepared by rapid melt quenching on a rotating disc [1]. The deformation
of metallic glass is inhomogeneous in nature at lower temperatures. Owing to the absence
of the long-range order, amorphous metallic alloys exhibit a very high yield stress
resulting in a very large accumulation of strain energy [2]. These glasses show very little
plasticity under tensile loading. Recently, several multi-component metallic alloys with an
excellent glass forming ability have been reported. Reduced cooling rates are sufficient to
achieve bulk samples in the amorphous state (e.g., rods a few millimeters in diameter) [3].
We present the fracture surface analysis of an amorphous ribbon prepared from the
Zr–Ti–Cu–Ni type of alloy, capable of achieving amorphous structure at lower cooling
rates.
Experimental. Samples made from a bulk amorphous alloy with the nominal
composition of Zr50Ti16.5Cu15Ni18.5 (at.%) were used in the experiments. The 300 �m thick
and 3–5 mm wide amorphous ribbons were prepared by rapid melt quenching on a
spinning metallic disc. The thickness of the prepared ribbon substantially exceeds the
maximum thickness of ribbons prepared from standard amorphous alloys. The amorphous
structure of a sample was confirmed by X-ray diffraction. Structure properties were
characterized by differential scanning calorimetry (Perkin Elmer DSC 7). Ribbons were
fractured by a tensile test on the machine with the stiffness of 10 kN/mm, the deformation
rate being 2610 3
. � � s �1 at 300 K. A scanning electron microscope Tesla BS340 was used
for fractographic observations.
Results and Discussion. A wide temperature region of undercooled liquid state
above the glass transition temperature Tg (592 K) up to the crystallization temperature
Tx (629 K) is typical for the amorphous alloy Zr50Ti16.5Cu15Ni18.5 as demonstrated by the
DSC thermogram in Fig. 1. The ribbon samples were loaded under uniaxial tension. The
measured fracture stress was 1.53�0.15 GPa which is similar to that reported in [4, 5].
The stress–strain curve for Zr50Ti16.5Cu15Ni18.5 at a strain rate of 2610 3
. � � s �1 at 300 K
under uniaxial tension is shown in Fig. 1 on the right side. Multiple serrations were
©J.MIŠKUF, K. CSACH, A. JURÍKOVÁ, V. OCELÍK, V. BENGUS, E. TABACHNIKOVA, 2008
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Failure of Zr50Ti16.5Cu15Ni18.5 Amorphous Metallic Ribbon
observed prior to failure. The origin of the serrated flow in metallic glasses is still unclear,
it is definitely related to the formation of shear bands. The formation of the individual
shear band is manifested in a single serration and all of the work done in producing the
shear band is dissipated as heat [6].
a b
Fig. 1. DSC trace of Zr50Ti16.5Cu15Ni18.5 at a heating rate of 20 K/min (a). Stress–strain curve at
strain rate of 26 10 3
. � � s �1 under uniaxial tension at temperature 300 K (b).
The observed macroscopic plastic deformation was just about 0.5%. The fracture is
localized in a major shear band and the fracture angle between the tensile stress axis and
the fracture plane is close to 45� – the failure in the maximum shear stress plane. The
reduced free volume results in the deviation of the shear banding direction from the
maximum shear stress [7].
The main fracture surface feature observed was the vein pattern morphology created
by the process of meniscus instability [8]. A ridge (vein) on the fracture surface results
from a connection of two adjacent cavities that grow under the action of external stress.
Such a vein pattern morphology shows a mirror image on two opposite sides of the
created fracture surface.
The left side of the fracture surface presented in Fig. 2a shows a vein free area
formed during an initial stage of the local shear at the wheel side of the ribbon. This area
corresponds to zone A of the scheme shown on the right side of Fig. 2. The scheme
summarizes all typical features observed on the fracture surface of 300 �m thick
amorphous ribbons with a wide undercooled liquid state region and fractured by ductile
shear failure.
a b
Fig. 2. Fracture surface in the vicinity of a sample edge. An intensive shear near the edge of the
fracture surface (a) and the scheme of areas with three characteristic morphologies observed on the
fracture surface of a 300 �m thick amorphous ribbon (b).
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J. Miškuf, K. Csach, A. Juríková, etal.
For standard amorphous metallic alloys in the form of ribbons the failure is initiated
mostly at surfaces and only occasionally at extraneous particles or intersections of shear
bands [9]. On the fracture surface of a 300 �m thick ribbon we observed the areas with
radial veins. These radial veins come out from the central flat area as Fig. 3a clearly
shows.
Similar morphology of radial veins was observed on Zr59Cu20Al10Ni8Ti3 bulk
amorphous alloy failed in tensile mode [10]. The fracture nucleates at the central flat part
as a consequence of two processes: (i) the nucleation and (ii) the propagation of cores. A
subsequent cavity growth proceeds through the formation of radial veins which become
finally linked to the main vein around the whole cell – Fig. 3a. The cell contains a flat and
radial parts enclosed with secondary vein rings of a cellular unit. No extraneous particles
or visible defects are present at flat centers.
a b
Fig. 3. Cellular vein-like morphology together with areas of radial primary veins – zone B (a).
“River morphology of fracture surface” corresponding to zone C of the scheme in Fig. 2b.
The fractographic analysis of ductile shear failure of a 300 �m thick amorphous
metallic ribbon has shown that its morphologic characteristics are close to the features
observed on the ductile fracture surface of bulk amorphous metallic materials in a wide
variety of forms [9]. The fracture surface is formed through the meniscus instability
process inside an adiabatic thin shear band.
A complex stress field at the final fracture stage forms distinct relief structures on
the fracture surface with a number of aligned veins. The relief fracture surface contains
ridges with the main vein at their tops and ditches between them – Fig. 3b. Aligned
primary veins propagate from the rivers to the ridges and link into the main one. This type
of the vein organization observed on the fracture surface of Pd40Cu30Ni10P20 bulk
amorphous alloy is called the river morphology of fracture surface [11]. Similar fracture
surface morphology of Zr-based bulk metallic glass matrix composites and Cu-based bulk
glass after compression testing was observed in [12]. However, the round cores with radial
veins were also observed in compression at elevated temperatures [13].
The tensile failure criterion [14] indicates that tensile failure is controlled by both the
normal stress � and the shear stress � (where � 0 is the normal fracture stress and � 0 is
the shear fracture stress):
2 2
� �
� � 1.
2 2
(1)
� �
0
However, the dependence of the shear stress � on the normal stress � is not linear
as the Mohr–Coulomb criterion. The influence of the normal stress presence during the
creation of zones B and C at failure causes the principal difference in the fracture surface
30 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
0

Failure of Zr50Ti16.5Cu15Ni18.5 Amorphous Metallic Ribbon
morphology between zone A and zones B and C. The smooth surface of zone A created
under the pure shear stress at the first stage becomes, due to increasing normal stress,
more multifarious (zone B). The increased influence of the normal stress in final stages of
deformation and failure and more complex deformation conditions associated with
serration on the loading-deformation curve leads to higher surface profile with ripples
(zone C). Similar distinguishing of fracture stages in the case of a polymer failure was
described in [15].
The results suggest that the catastrophic fracture is no longer a pure shear process,
whereas the normal stress plays a remarkable role.
Conclusions. The fractographic analysis of the fracture surface of Zr50Ti16.5Cu15Ni18.5
amorphous metallic alloy in the form of a 300 �m thick ribbon fractured in tensile tests
reveals the presence of shear failure by the meniscus instability mechanism. Features
similar to the fracture morphology of bulk amorphous alloys are formed in the catastrophic
shear band and presented on the fracture surface.
We have described three different distinct pattern morphologies. Primary progressive
sliding in the first region (A) is followed by the general fracture that consists of two
regions. The presence of the vein-like pattern with frequent radial vein forms is typical of
the second fracture region (B). The last – third – region of the fracture surface (C) has a
more pronounced relief and is covered with a river-like pattern. The vein-like pattern of
the second region covers a dominant part of the final fracture surface.
Acknowledgment. This work was supported by the Slovak Grant Agency for Science –
VEGA.
1. P. Duhaj, P. Svec, E. Majkova, et al., Mater. Sci. Eng., A133, 662 (1990).
2. Y. Zhang and A. L. Greer, Appl. Phys. Lett., 89, art. 071907 (2006).
3. A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans. JIM, 31, 177 (1990).
4. G. Abrosimova, A. Aronin, D. Matveev, et al., J. Mater. Sci., 36, 3933 (2001).
5. W. Zhang and A. Inoue, Scripta Mater., 48, 641 (2003).
6. W. J. Wright, R. B. Schwarz, and W. D. Nix, Mat. Sci. Eng., A319-A321, 229 (2001).
7. W. H. Jiang, G. J. Fan, F. X. Liu, et al., J. Mat. Res., 21, No. 9, 2164 (2006).
8. F. Spaepen, Acta Metall., 23, 615 (1975).
9. V. Z. Bengus, E. D. Tabachnikova, J. Miškuf, et al., J. Mat. Sci., 35, 4449 (2000).
10. Z. F. Zhang, J. Eckert, and L. Schultz, Acta Mater., 51, 1167 (2003).
11. Ch. Ma and A. Inoue, Mater. Trans. JIM, 43, 3266 (2002).
12. M. Kusy, U. Kuhn, A. Concustell, et al., Intermetallics, 14, 982 (2006).
13. G. Wang, J. Shen, J. F. Sun, et al., Mat. Sci. Eng., A398, 82 (2005).
14. Z. F. Zhang and J. Eckert, Phys. Rev. Lett., 94, art. 094301 (2005).
15. J. Fineberg, S. P. Gross, M. Marder, and H. L. Swinney, Phys. Rev. Lett., 67, No. 4, 457
(1991).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 31

UDC 539. 4
Small Punch Testing and Its Numerical Simulations under Constant
Deflection Force Conditions
P. Dymáèek 1,a and K. Milièka 1,b
1
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech
Republic
a b
pdymacek@ipm.cz, milicka@ipm.cz
A comparison of results of small punch tests on miniaturized discs under a constant force with their
simulation by means of FEM is presented. A heat resistant steel of type CSN 41 5313 (EN 10CrMo9-10)
was selected for our investigations. The small punch tests as well as the necessary conventional creep
tests on massive specimens were performed at 873 K. For simulations, the Norton power-law and
the exponential relationships were applied in the FEM model of the SPT arrangement. Parameters
of both relationships were derived from stress dependences of minimum creep rate obtained from
the conventional creep tests. While at higher loads the Norton power-law yields results more
comparable with those obtained from experiments, at lower loads the exponential relationship gives
better results. The investigation also confirms the simple relation between stress in conventional
tests and force in small punch tests resulting in identical time to fracture of both types of tests.
Keywords: small punch test, finite element method, parametric study, creep, fracture
mechanics.
Introduction. Small punch tests (SPT) on thin disk specimens can be considered as
one of the promising methods for the determination of the residual – or at least guaranteed –
life of exposed parts of power generation and thermal facilities. Due to small specimen
dimensions it may be classified as a non-destructive method in this industrial sector.
Recently, there have been significant efforts by European and US research groups to
standardize the dimensions and test conditions of SPT at low, ambient, and high
temperatures [1]. Currently, a good progress has been achieved in the numerical modeling
of the SPT at room and low temperatures, for the SPT at constant deflection rate
conditions [2, 3]. Preliminary results at IPM demonstrated that SPT-CDF (at constant
deflection force conditions) represent an apt tool for obtaining local creep properties at
operational temperatures. It was shown that the results of these tests can be correlated
with the results of conventional tests on massive specimens [4, 5]. Thus, the small punch
technique should provide important information for safety procedures. However, the
currently applied relations between results of conventional testing and small punch tests
are purely empirical. The aim of this work was to apply the finite element method (FEM)
for the verification and better understanding of the small punch test application in the
assessment of the creep resistance and either the residual or guaranteed life time for heat
resistant steels.
Procedures. The material chosen for this study was a low alloy heat resistant steel
CSN 415313 (EN equivalent 10CrMo9-10), which is widely used in the Czech power
generation industry. The testing temperature was set to be 600�C (873 K), which is the
maximum recommended operation temperature for this steel in long-term service. In order
to obtain accurate relationships between the results of conventional and small punch tests,
the comparison of their results obtained on the same heat of steel with identical heat
treatment as well as mechanical treatment was necessary. Therefore, both types of tests
were performed under conditions leading to comparable values of time to rupture (up to
1000 hr). Stress (load) ranges were 80 to 200 MPa for conventional creep tests and 200 to
500 N for SPT. Several conventional tensile tests at the testing temperature were also
performed in order to determine the static material properties, namely the Young modulus.
©P.DYMÁÈEK, K. MILIÈKA, 2008
32 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Small Punch Testing and Its Numerical Simulations ...
Results and Discussion. A comparison of the experimental values of the force F
and the stress � resulting in identical time to fracture in both types, i.e., SPT, and
conventional creep tests (see Fig. 1) confirmed the simple relation between the force and
stress in the form [4, 5]:
F ���, (1)
where the factor � reaches values close to 2.6 for some heat-resistant steels. The value
��2.5 was obtained from the present experiments. The plot of experimental and
numerical results shown in Fig. 2 will be discussed further.
Fig. 1 Fig. 2
Fig. 1. Comparison of the load and stress at identical time to fracture for conventional creep tests
and SPT.
Fig. 2. Comparison of the load vs. time to fracture for experimental and calculated SPT data.
Fig. 3 Fig. 4
Fig. 3. A 2D axisymmetric FE model of the SPT arrangement, expanded to 3D.
Fig. 4. Equivalent creep strain plot for a specimen loaded with F � 500 Natt � 13,525 s.
A two-dimensional axisymmetric model of the SPT arrangement was formulated in
the ANSYS FEM system [6]. The model is shown in Figs. 3 and 4. The contact between
the specimen and arrangement was modeled using surface to surface contact elements
with the friction coefficient f � 0.1. The parametric study of various friction conditions
for SPT under constant deflection rate was done in [7]. Application of two types of
constitutive creep models in the numerical analysis was performed using the Norton
power-law (Eq. (2)) and the exponential relationship (Eq. (3)):
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 33

P. Dymáèek and K. Milièka
and
�� � B�
(2)
cr
n
� / m
� � � Ce .
(3)
cr
Both of these equations are applicable mostly to the secondary creep rates. From the
regression analysis of the conventional creep test data we obtained the coefficients
B � � �
3257 10 21
. , n� 6.505 for the Norton power-law and C � � �
26810 10
. , m� 21.4 for
the exponential form.
The load cases were numerically solved for the identical number of load levels as the
performed SP testing. The experimental SPT curves at two different load levels and the
relevant calculated curves are compared in Figs. 5 and 6. The experimental SPT curves
for the repeated tests at a load level of 500 N are shown in Fig. 7, they demonstrate an
acceptably small scatter.
Fig. 5 Fig. 6
Fig. 5. Experimental and calculated SPT curves at F � 500 N.
Fig. 6. Experimental and calculated SPT curves at F � 300 N.
Fig. 7 Fig. 8
Fig. 7. Experimental SPT curves at F � 500 N, illustration of test reproducibility.
Fig. 8. Experimental and calculated SPT deflection rate curves at F � 300 N.
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Small Punch Testing and Its Numerical Simulations ...
A very good correlation of time to fracture was obtained for the Norton constitutive
model, the exponential model gives too conservative results for high load levels and
non-conservative ones for lower load levels (see Fig. 2). In spite of this, for lower load
conditions the exponential model provides a better fit of the analysis results with the
experiment at the primary and secondary creep stages (as shown in Fig. 6). A comparison
of creep deflection rates for load F � 300 N between the test and numerical analysis
results is shown in Fig. 8.
The FE model does not include any damage modeling. Therefore, the tertiary part of
the calculated creep diagram is driven mainly by the geometrical softening (a local
decrease in the specimen thickness). This leads to a slightly different shape of the tertiary
region of the creep curve as compared to the test data. However, it does not seem to
influence substantially the calculated life-time to be much different from the life-time
measured on the specimen. Implementation of the damage modeling, for example with the
use of a so-called element death technique or application of creep constitutive models that
account for damage, could further improve the capabilities of the SPT FE model in order
to describe more realistically the tertiary creep stages.
Conclusions. The SPT under constant deflection force can be well simulated by
means of the finite element method and relatively simple creep constitutive models such
as the Norton power-law or the exponential relationship. The adequacy of the calculated
results can be further improved either by including the damage modeling in the SPT
model or using more complex constitutive models that can well describe all three creep
stages of the material behavior.
1. Small Punch Test Method for Metallic Materials. Part A: A Code of Practice for Small Punch
Creep Testing. Part B: A Code of Practice for Small Punch Testing for Tensile and Fracture
Behavior, Documents of CEN WS21, Brusseles (in press).
2. M. Abendroth and M. Kuna, Eng. Fract. Mech., 73, 710 (2006).
3. C. Sainte Catherine, J. Messier, Ch. Poussard, et al., in: M. A. Sokolov, J. D. Landes, and
G. E. Lucas (Eds.), Small Specimen Test Techniques, Fourth Volume, American Society for
Testing and Materials, West Conshohocken, PA (2002), p. 350.
4. K. Milièka and F. Dobeš, Mat. Sci. Forum, 482, 407 (2004).
5. K. Milièka and F. Dobeš, Int. J. Press. Vess. Piping, 83, 625 (2006).
6. ANSYS 9.0 Release Documentation, SAS IP (2004).
7. P. Dymáèek, New Methods of Damage and Failure Analysis of Structural Part, TU Ostrava,
Czech Republic, September 4–8 (2006), ISBN 80-248-1126-0, p. 269.
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 35

UDC 539. 4
Constitutive Description of Creep Behavior of Mg–4Al–1Ca Alloy
K. Milièka 1,a and F. Dobeš 1,b
1
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech
Republic
a milicka@ipm.cz, b dobes@ipm.cz
Creep behavior of an advanced magnesium alloy AX41 (4 wt.% Al, 1 wt.% Ca, Mg balanced) was
investigated in temperature interval from 343 to 673 K and stresses from 2 to 200 MPa.
Compressive creep experiments with stepwise loading were used in order to obtain stress
dependence of the creep rate in interval from 10 9
� to 10 3 � s �1 for a given temperature. All stress
dependences can be well described by the Garofalo sinh relationship with natural exponent n � 5.
An analysis of the parameters of this relationship has shown that lattice diffusion controls creep at
all experimental conditions. While climb-controlled creep mechanism is decisive at lower stresses
and higher temperatures, glide-controlled mechanisms act at higher stresses and lower temperatures.
A typical power-law breakdown is observed at intermediate stresses and temperatures.
Keywords: magnesium alloys, creep, constitutive creep equation of creep, creep
mechanisms.
Introduction. The Mg–Al–Ca alloys are developed as a cheaper alternative of the
alloys containing rare earth metals for applications at elevated temperatures. Mechanical
properties of these alloys, namely their creep resistance, are improved by precipitates of
Mg17Al12 and Mg2Ca. However, effective development of this type of magnesium alloys is
impeded by the lack of experimental data as well as detailed knowledge of mechanisms
governing their creep behavior at elevated temperatures. In the present study, some results
of creep behavior investigation of a representative of this alloy group, i.e., the alloy
AX41, are summarized for a wide interval of temperatures and stresses.
Experimental. Magnesium alloy AX41 with nominal composition (in wt.%) 4 Al,
1 Ca and Mg balanced was cast in Zentrum für Funktionwerkstoffe in Clausthal-
Zellerfeld, Germany. Parallelepiped specimens with 6�6 mm cross section and 12 mm
height were annealed at 673 K for 24 h and cooled in air and then heated at 353 K for 16 h.
The average size of regular grains d � 0.037 mm resulted from the high temperature
treatment.
Compressive creep tests with stepwise loading were used, in order to obtain stress
dependence of the creep rate in interval from 10 9 � to 10 3 � s �1 for a given temperature. In
any step, the constant loading was hold until the creep rate reached stationary or
quasi-stationary value. This rate was then assigned to the true stress � corresponding to
the last strain value in the step. The loadings of consequent steps were chosen randomly.
The tests were mostly conducted till the strain reached a value �� 0.15. Suitability of the
used stepwise procedure was verified by a comparison of obtained creep rates at a given
stress level with those resulting from conventional compressive tests under constant stress.
Differences of these values lay in scatter error.
The tests were performed in purified and dried argon atmosphere. Identical
temperature regime was applied before each test in order to eliminate eventual influence
of temperature on second phase’s precipitation during the test. In all cases, the sample was
kept approximately 10 h at the testing temperature before the test was started. The strain
was measured with the sensitivity 10 5 � . For the stepwise stress creep experiments and
evaluation of their results, special software was developed.
© K. MILIÈKA, F. DOBEŠ, 2008
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Constitutive Description of Creep Behavior of Mg–4Al–1Ca Alloy
Results. Creep behavior of the alloy was investigated at temperatures from 343 to
673 K. Stress dependences of the creep rate �� are illustrated in both conventional
coordinate systems, i.e., bi- and semi-logarithmic, in Fig. 1a and 1b. From the shape of
dependences, no simple relationships, power law or exponential, can be chosen for their
description in the entire experimental interval of conditions. For small stresses and higher
temperatures the Norton power-law relation
���� n (1)
with n� 5 seems to be suitable for the description, the exponential relationship can be
rather well applied at lower temperatures and higher stresses. At intermediate testing
conditions, neither of both relationships is applicable. In principle, such behavior can be
well described by Garofalo’s sinh formula, which is conforming to both these basic
descriptions in accord with above stress dependence of the rate ��.
a
b
Fig. 1. Stress dependences of creep rate in bi-logarithmic (a) and semi-logarithmic (b) coordinates.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 37

K. Milièka and F. Dobeš
The Garofalo equation has a form [1]
� ��A(sinh[ B�])
,
where parameters A and B depend on temperature T only and exponent n is
considered to be natural number and temperature dependence of the parameter A can be
written as
Q
A � �
RT
� �
exp ,
�� ��
(3)
where Q is the activation energy and R the gas constant. For values B��0.8, Eq. (2)
transfers to power-law relationship with stress exponent n and for B��1.2 to the
exponential relationship with the function argument nB�.
Values of the exponent n from 3 to 7 were proved in data treatment. Statistically, the
best agreement was obtained by description for the exponent n� 5. Using this value,
optimum treatment of the stress dependences of the rate �� has confirmed good
applicability of both Eqs. (2) and (3) – see drawn curves in Fig. 1a and 1b which
correspond to these equations.
Dependence of the parameter A on reciprocal temperature is plotted in Fig. 2. A
straight line can be drawn through calculated values in chosen coordinate system, which
confirms validity of Eq. (3). The activation energy Q� 137 kJ/mol results from the slope
of the straight line. This value is very close to the activation enthalpy of self-diffusion of
magnesium �H SD � 135 kJ/mol [2].
Temperature dependence of the parameter B is plotted in the Fig. 3. The dependence
has a convex shape; the parameter B reaches values from 0.021 to 0.035 with the
minimum at approximately at 450 K.
Fig. 2 Fig. 3
Fig. 2. Temperature dependence of the parameter A.
Fig. 3. Temperature dependence of the parameter B.
Discussion. The activation energy Q obtained from temperature dependence of
parameter A [cf. Fig. 2 and Eq. (3)] is very close to the activation enthalpy of lattice
diffusion in Mg. Probably, there are no data of diffusion in the investigated magnesium
alloy AX41. However, it can be expected that the enthalpy of lattice diffusion in the
investigated alloy does not differ substantially from that in pure magnesium. Therefore,
one can assume that the value of the energy Q supports an expectation that the creep
behavior of the alloy is controlled by diffusion processes under all experimental conditions.
38 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
n
(2)

Constitutive Description of Creep Behavior of Mg–4Al–1Ca Alloy
A natural exponent n� 5 was revealed to be the most convenient stress exponent in
the power-law part of the stress dependences of the creep rate ��. From phenomenological
point of view, such exponent is usually connected with the metal-type (Class II) creep
behavior [3]. As the most probable mechanism controlling creep, respecting also the value
of the energy Q, combined mechanism of climb and glide of dislocations can be
considered (see e.g., [4]).
Exponential expression of the stress dependences of rate �� is frequently attributed to
thermally activated glide of dislocations. With respect to the controlling role of lattice
diffusion, the non-conservative glide should be the major mechanism in the interval of the
validity of exponential dependence. A very simple concept of non-conservative motion of
jogs on screw dislocation segments [5] can be accepted. Then, the apparent activation
energy of creep QcRT �� [ ln � � � �( 1 )] � should depend on the stress due to the
temperature dependence of the parameter B.
It can be seen from Fig. 1a that the shape of stress dependences at the highest
temperatures indicates possible threshold behavior since a strong bend of the rate ��
towards lower values appears when the stress decrease to a certain value (~ threshold
stress � th ). Therefore, an attempt was performed to describe these dependences by the
modified Garofalo relationship
�� � A{sinh[ B( ���th )]} ,
which are illustrated in Fig. 1a by dashed lines drawn for 673 and 623 K. However,
acceptable positive values of � th were obtained from optimizing procedures only at
temperatures from 473 to 673 K.
Conclusions. Following conclusions can be drawn from the investigation of creep
behavior of the AX41 alloy in temperature interval from 343 to 673 K:
� Stress dependences of the minimum creep rate �� can be well described by the
Garofalo equation (2).
� Obtained parameters of this relationship can be well physically interpreted.
� Lattice diffusion controls creep behavior of the AX41 alloy in the entire
experimental interval.
Acknowledgment. The work was supported by Project 106/06/1354 of the Grant Agency of
the Czech Republic.
1. G. Garofalo, Trans. AIME, 227, 351 (1963).
2. P. G. Shewmon, Trans. AIME, 206, 918 (1956).
3. O. D. Sherby and P. M. Burke, Prog. Mat. Sci., 13, 325 (1968).
4. H. J. Frost and M. F. Ashby, Deformation-Mechanisms Maps. The Plasticity and Creep of
Metals and Ceramics, Chapter 2, Pergamon Press, Oxford (1982).
5. J. Èadek, Creep in Metallic Materials, Chapter 9, Elsevier, Oxford; Academia, Prague (1988).
5
(4)
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 39

UDC 539. 4
Fatigue Lifetime of ADI from Ultimate Tensile Strength to Permanent
Fatigue Limit
J. Zapletal, 1,a S. Vìchet, 1,b J. Kohout, 2,c and K. Obrtlík 3,d
1 Brno University of Technology, Brno, Czech Republic
2 University of Defence, Brno, Czech Republic
3
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech
Republic
a pepa.sanguis@centrum.cz, b vechet@fme.vutbr.cz, c jan.kohout@unob.cz, d obrtlik@ipm.cz
S�N curve of austempered ductile iron was obtained in the range of lifetime including low cycle
fatigue domain and high cycle fatigue domain up to 10 8 cycles. Ultimate tensile strength is used as a
limiting value of the curve. Symmetric push-pull fatigue and tensile tests were performed at room
temperature on isothermally treated nodular cast iron alloyed with copper and nickel having
positive impact on mechanical, technological and fatigue properties of austempered ductile iron.
Suitable functions for the fit of experimentally determined points were tested and their parameters
were calculated. The best results were obtained using the Palmgren function and the function
introduced by Kohout and Vechet. Since the loading frequency in high-cycle region is two orders
higher than in low-cycle region, the effect of loading cycle frequency on fatigue behavior of the
studied material is also studied. A possibility of discontinuity of experimental data between
low-cycle and high-cycle regions is discussed.
Keywords: austempered ductile iron, fatigue behavior, S�N curve, fatigue limit, low-cycle
fatigue tests, high-cycle fatigue tests, regression.
Introduction. Nodular cast iron and its isothermally heat treated variant, austempered
ductile iron (ADI), are structural materials applied in many branches of mechanical and
civil engineering and transportation. Comparing with other sorts of cast iron, its advantage
consists in favorable shape of graphite, which enables full exploitation of mechanical
properties of the metal matrix. Recently ADI has been used for the production of
crankshafts, engine blocks, rotors of electric generators, gas compressor casings, large
gears, pressing dies, wheels of colliery cars, etc. [1].
Experimental. The test bars for static mechanical tests in tension as well as for
fatigue tests were made of keel blocks of alloyed nodular cast iron. Its chemical
composition determined using quantometer is presented in Table 1. Isothermal heat
treatment resulting in a bainitic structure was performed in electric pot furnaces containing
salt bathes. Austenization was realized in the salt bath at a temperature of 900�C for1h.
Isothermal decomposition was performed in the AS 140 salt bath at 400�C during 50 min
with aftercooling in water. The matrix of the material studied consisted of upper bainite
and stabilized retained austenite, whose content was determined using quantitative phase
X-ray analysis to be 39 vol.%. For the determination of the basic mechanical properties
at static tensile loading, cylindrical test bars 6 mm in diameter were tested. The elongation
of the test bars was measured by an extensometer with a gauge length of 30 mm. Tests
were performed using a Mod. TiraTest 2300 PC-controlled testing device at a stress rate
of 30 MPa/s. The basic stress and strain characteristics are summarized in Table 2.
For the assessment of low-cycle parameters the threaded bars of diameter 8 mm and
a gauge length of 12 mm were used. They were loaded using MTS 810 electro-hydraulic
PC-controlled test system in the regime of a controlled loading force with a symmetric
sinusoidal push-pull course at an average stress rate of 4000 MPa/s. Deformation was
measured using an axial extensometer with a gauge length of 12 mm. Also, high-cycle
© J. ZAPLETAL, S. VÌCHET, J. KOHOUT, K. OBRTLÍK, 2008
40 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

fatigue tests were performed using 7-mm-diameter bars with threaded heads. A Mod.
Amsler HFP 1478 high-frequency pulsator was used to load the bars with a symmetric
push-pull loading cycle with a frequency of about 200 Hz. All fatigue tests as well as
static tensile tests were carried out at room temperature.
Table 1
Chemical Composition of Nodular Cast Iron under Study
Element C Mn Si P S Ni Cu Mg
wt.% 3.80 0.37 2.22 0.024 0.002 0.49 0.31 0.057
Table 2
Data Processing of Experimental Results. The experimentally obtained dependence
of the stress amplitude �( N ) on the number of cycles to fracture N in the range from 0.5
to 10 8 cycles was fitted using two different regression functions: the Palmgren function
[2]
�( N) a( N B) �
b
� � � � (1)
and the Kohout–Vìchet function [3]
Fatigue Lifetime of ADI from Ultimate Tensile Strength ...
Static Mechanical Characteristics of ADI in Tension
Material Rp02 . , MPa Rm , MPa A, % Z, %
ADI 400�C/50 min 636 976 11.4 9.7
�N�B�
�( N ) � ��
� � ,
�N�C�
where a, b, B, C, and � � are the regression parameters. The meaning of all parameters
is unequivocal and with a close relation to geometrical shape of the curve only in the case
of the Kohout–Vìchet function: � � means the permanent fatigue limit for an infinite
number of cycles to fracture (giga-cycle fatigue is not considered here), B and C
represent the positions of curve bends, and b is the curve slope at the point of inflexion
when the curve is plotted in the log–log scale. In the case of the Palmgren function, the
relation between parameter b and the slope is not so direct and the parameter a has a
rather complicated meaning.
Test Results and Discussion. The experimental dependence of the stress amplitude
on the number of cycles to fracture was fitted using both Eq. (1) and (2), see Figs. 1, 2,
and 3, where both fits are compared. The values of regression parameters together with
the calculated fatigue limit for 10 7 cycles to fracture and the sum of squares of deviations
between measured and fitted values S are presented in Table 3.
The difference in fits using different regression functions is evident at first sight: Eq.
(2) leads to a better fit than Eq. (1) does. This first impression is supported by the values
of the sums of squares: for Eq. (2) only 72% of the value corresponding to Eq. (1) is
obtained. Moreover, two regions of the numbers of cycles to fracture are better described
using Eq. (1): the low-cycle region from 10 2 to 10 5 cycles and the high-cycle region
above 10 7 cycles. It means that Eq. (2) has a better limiting behavior than that of Eq. (1).
Quantitatively it can be best expressed by the standard deviations of the parameter � �
representing the limiting behavior of both equations: it was calculated to be � � � (226.9
�30.3) MPa for Eq. (1) and � � � (310.1�8.8) MPa for Eq. (2).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 41
b
(2)

J. Zapletal, S. Vìchet, J. Kohout, and K. Obrtlík
Table 3
Results of Regression Calculations
Parameter �� , MPa b B a, MPa or C �C , MPa S
Eq. (1) 226.9 �0.1882 65.02 1627.62 305.2 20,543
Eq. (2) 310.1 �0.1086 33.11 1212,180 314.0 14,738
Fig. 1. S�N curve of the studied ADI, fitted by the Palmgren function (1).
Fig. 2. S�N curve of the studied ADI, fitted by the Kohout–Vìchet function (2).
Discontinuities between a low-cycle and high-cycle regions are often reported not
only as results of experimental tests [4, 5] but also as conclusions of theoretical
considerations [6, 7]. However, in Figs. 1, 2, and 3 both the low- and high-cycle results
are plotted commonly and it can be seen here that no discontinuity exists between them.
Even in two orders of the number of cycles to fracture the low- and high-cycle
experimental points overlap and their link-up is ideal, without any sign of break or shift. It
can serve as an indirect evidence that both types of tests were performed correctly and
responsibly.
42 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Fatigue Lifetime of ADI from Ultimate Tensile Strength ...
Fig. 3. Comparison of the fits by the Palmgren function (1) and by the Kohout–Vìchet function (2).
Generally, it is very hard to tell if the above-mentioned discontinuities are only
experimental artefacts or if they can have a principal cause. It is most probable that at
least in some cases the discontinuities can be attributable to changed experimental
conditions, inaccurate measurements or incorrect conversion between low-cycle and
high-cycle data.
Conclusions
1. No discontinuity was found between the low- and high-cycle regions in
experimental results of ADI studied, even when the loading frequencies differ by two
orders of magnitude (1 to 200 Hz).
2. The experimental fatigue test results in the whole range of the number of cycles to
fracture can be fitted using the Palmgren function and the Kohout–Vìchet function. The
latter provides a better fit in a low-cycle as well as high-cycle regions.
3. A relatively high value of the fatigue limit �C � 314 MPa means that the
optimum regime of heat treatment was applied.
Acknowledgements. The financial supports by the Ministry of Defense of the Czech Republic
within the Research Project No. MO0FVT0000404 and by the Grant Agency of the Czech Republic
within the Grant Project No. 106/03/1265 are gratefully acknowledged.
1. E. Dorazil, High Strength Austempered Ductile Cast Iron, Horwood, London (1991).
2. W. Weibull, Fatigue Testing and Analysis of Results, Pergamon Press, London etc. (1962).
3. J. Kohout and S. Vìchet, Int. J. Fatigue, 23, 175 (2001).
4. D. S. Matsumoto and S. K. Gifford, J. Mater. Sci., 20, 4610 (1985).
5. R. Boukhili and R. Gauvin, J. Mater. Sci. Lett., 9, 449 (1989).
6. J. Pokluda, F. Kroupa, and L. Obdr�álek, Mechanical Properties and Structure of Solids [in
Czech], PC-DIR, Brno (1994).
7. A. Puškár and M. Hazlinger, Failure and Fractures of Details [in Slovak], University of
�ilina, �ilina (2000).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 43

UDC 539. 4
Deformation Resistance and Structure-Forming Processes of Iron Aluminides
in Hot Rolling
P. Suchánek, 1,a I. Schindler, 1 P. Kratochvíl, 2 and P. Hanus 2,b
1
Institute of Modeling and Control of Forming Processes, VŠB – Technical University of Ostrava,
Ostrava-Poruba, Czech Republic
2 Department of Material Science, Technical University of Liberec, Liberec, Czech Republic
a pavel.suchanek@vsb.cz, b pavel.hanus@tul.cz
We have developed simple mathematical models of mean equivalent stress dependence on
temperature and strain for selected iron aluminides. Four similar melts with 16.5–19.2 wt.% of Al,
4 wt.% of Cr and with various contents of Ti and B were studied and compared. Flat specimens
graded by thickness were hot rolled. Deformation resistance was calculated from the roll force
values obtained using a laboratory mill Tandem. Postdynamic structure-forming processes of the
tested aluminides, as well as their cracking susceptibility, were investigated by metallography. The
differences in the deformation behavior and formability of the tested aluminides were described.
Keywords: iron aluminides, hot rolling, deformation resistance, microstructure, formability.
Introduction. Fe3Al-based iron aluminides have been an object of investigation for
many years. These alloys feature low material costs and a lower specific weight.
Compared with expensive corrosion-resistant types of steel, they guarantee savings in
elements, such as Cr, Ni, and some others. Their tensile strength is comparable with that
of many other steels. They have a high resistance in sulphidic and oxidic atmospheres,
especially at high temperatures, and therefore, are promising materials for manufacturing,
e.g., structural parts for aviation, heating elements, heat exchangers, equipment for
chemical production, etc. [1].
A problem with Fe3Al-based materials consists in their preparation and subsequent
processing. They feature brittleness at the ambient temperature and a drop of strength
above 600�C, which was the reason for not using them as structural materials. Attention
has recently been focussed mainly on utilization of corrosion-resistant properties of iron
aluminides at high temperatures. An essential step forward in their application is an
increase in their creep resistance at temperatures above 600�C. This is achieved by the
additives that form stable phases thus increasing the strength of the material at the
temperatures of their operation. However, this strengthening may adversely affect the
production of components, as the case may be, e.g., during hot forming. It is the
introductory experiments involving determination of the deformation resistance of iron
aluminides hardened for a later application as the materials exhibiting creep resistance at
high temperatures that are the subject of this work.
Experimental. Four melts of iron aluminides with similar chemical compositions
and various contents of Cr, Ti, and B (Table 1) were studied and compared. The chromium
content in the range from 2 to 5 at.% has no effect on the basic mechanical properties of
the aluminide, and its function is only to improve the formability at lower temperatures
[1]. The experiment was divided in two parts. First, the mean equivalent stress (MES) was
determined using a laboratory rolling mill Tandem, and then postdynamic structureforming
processes in the investigated aluminides rolled in a laboratory rolling mill K350
were studied [2].
Mean Equivalent Stress. Flat specimens graded by thickness, which have been
prepared by water cutting and grinding, were hot rolled. Each specimen was carefully
measured and afterwards directly heated in an electric resistance furnace to the rolling
© P. SUCHÁNEK, I. SCHINDLER, P. KRATOCHVÍL, P. HANUS, 2008
44 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

temperature (900–1200�C). The heated specimen was immediately rolled down in the mill
A of the laboratory mill Tandem [2] (roll diameter approx. 159 mm). The roll forces and
actual revolutions of the rolls were recorded using a computer. After cooling down of the
rolled stock, the width and thickness of individual specimens were also measured. All the
recorded variables mentioned above were presented in the table and recalculated to obtain
the values of the equivalent (logarithmic) height reduction e h , strain rate �e (in s �1 ) and
MES � m (in MPa) [3].
The resulting equation for the description of the MES should make possible a quick
prediction of the force parameters during adaptive control of the rolling mill. Based on
previous experience, a simple model for the description of the MES of the investigated
material in relation to strain (strengthening and dynamic softening are taken into account),
temperature and strain rate, which is dependent on the deformation, was chosen [4]:
v
e�
r
� eh
,
l
2
3
where vr (in mm/s) is the actual peripheral speed of the rolls with radius R (in mm), and
ld (in mm) represents the roll bite length. For calculation of the MES, the following
relationship was chosen:
B
� mc � Aeh exp( �Ce D
)� e exp( �GT),
(2)
where � mc (in MPa) is the mean equivalent stress (c means “as calculated”). During
calculation of the material constants A, ..., G (by means of the statistical software
UNISTAT 5.5) appearing in the equation of type (2), an observation was made for all the
materials studied (M1, M2, M3, and M4) that enabled us, without any registered loss of
accuracy, to simplify this relation by exclusion of the strain member. The following
models were the result of this mathematical processing:
0. 032
� mc �2017e�exp( �000225
. T)
0159 .
� mc �6763e�exp( �000395
. T)
0. 040
� mc �4954e�exp( �000311
. T)
0. 083
� mc �8832e�exp( �000389
. T)
Deformation Resistance and Structure-Forming Processes ...
Table 1
Chemical Composition of the Investigated Iron Aluminides in wt.%/at.%
Alloy Al Cr Ti B C
M1 16.5/28.9 4.0/3.6 TiB2 = 0.33/0.76 – 0.01/0.04
M2 19.2/32.8 4.9/4.3 0.68/0.65 – 0.04/0.12
M3 16.8/29.3 4.0/3.6 – 0.06/0.27 0.02/0.08
M4 18.4/31.7 4.9/4.4 0.61/0.59 0.07/0.30 0.02/0.08
d
h
(1)
for M1, (3)
for M2, (4)
for M3, (5)
for M4. (6)
The simplified models of the MES according to Eqs. (3)–(6) do not include the
strain parameter e h , which is sufficiently represented in the parameter of the strain rate �e
[see Eq. (1)], as it has already been found and verified by previous experiments [3].
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 45

P. Suchánek, I. Schindler, P. Kratochvíl, and P. Hanus
The accuracy of the obtained models can be evaluated by a simply defined relative
error (in %) according to the relation: ( �m��mc ) �m�100,
where � m and � mc are the
observed and calculated values of the mean equivalent stress, respectively. Relative errors
did not exceed approx. �10% for alloys M1 and M3 or �7% for alloys M2 and M4,
which is quite sufficient for the given purposes.
The mathematical model of the MES calculated on the basis of the methodology
mentioned above is capable to compare different deformation behaviour of the materials
M1–M4. For this purpose, graphs in Fig. 1 were plotted. It follows from Fig. 1 that alloys
M2 and M4, on the one hand, exhibit a sharper rise in the � m value with increasing strain
as against alloys M1 and M3, and on the other hand, their deformation resistance is
approx. 20 to 30 MPa lower. Moreover, for alloys M2 and M4, a decrease in the MES
with increased forming temperature is more pronounced.
a b
Fig. 1. Comparison of behavior of M1–M4 alloys in dependence on (a) height strain eh [see Eq. (1)
for dependence e� � f( eh) ] and (b) temperature T.
Evaluation of Microstructure. The forming temperatures used for all four aluminides
were 900, 1100, and 1300�C, and for alloy M3 a temperature of 1200�C was used
additionally. Specimens were rolled with one draught (height reduction) in the rolling mill
K350, the rotation speed of the rolls was 80 rpm. The relative height reduction
corresponded to a value of 33%.
Immediately after rolling, three modes of cooling were applied: quenching of the
specimen in oil directly or after a dwell at the forming temperature during 1 minute or 5
minutes. The resulting microstructure was analyzed by means of optical metallography
(Figs. 2 and 3).
Summary of Results. Figure 2 shows an example of the structure evolution
depending on the mode of cooling for the chosen iron aluminide M3. This example proves
the observation common for all four investigated materials that recrystallization proceeded
only in during the temperature dwell. Hence, softening of the investigated alloys by static
recrystallization has become apparent.
Rolling at a temperature of 1100�C followed by a1or5mindwell at the same
temperature (Fig. 2b, c and Fig. 3c) seemed to be the best way of forming from the
viewpoint of the deformed structure. A more pronounced refining of the structure due to
recrystallization occurred in the areas of more intensively formed edges of specimens.
Rolling at a temperature of 900�C led to only average-level recrystallization processes,
which can be seen from the photo in Fig. 3b). Rolling at a temperature of 1300�C did not
result in grain refinement because, during subsequent temperature dwell, a complete
recrystallization and subsequent grain coarsening occurred virtually to the original size
corresponding to the initial state (compare the photos in Fig. 3a and 3d).
Based on laboratory rolling of flat specimens graded by thickness, the values of � m
were obtained for iron aluminides M1, M2, M3, and M4 – after recalculation from roll
forces – namely in the range of logarithmic height strain e h from 0.20 to 0.76 and strain
rate �e from 20 to 96 s �1 . The rolling temperature T was in range from 960 to 1200�C.
46 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Deformation Resistance and Structure-Forming Processes ...
a b
c
Fig. 2. Comparison of structure evolution in case of selected M3 samples depending on schedule of
cooling from deformation temperature 1100�C: (a) 1100�C/oil quenching; (b) 1100�C/1 min, oil
quenching; (c) 1100�C/5 min, oil quenching.
a b
c d
Fig. 3. Structure of selected samples of M2 alloy: (a) initial state; (b) 900�C/5 min, oil quenching;
(c) 1100�C/5 min, oil quenching; (d) 1300�C/5 min, oil quenching.
As far as the accuracy of the derived models of the MES is concerned, for M1 alloy
the root-mean-square error was 17.3 and the value of R 2 � 0.91; for M2 alloy the
respective magnitudes were 6.1 and 0.97; for M3 alloy 9.9 and 0.95; and for M4 alloy
10.1 and 0.95. It may be concluded that the scatter of deviations between the values of
� m obtained from the experiments and recalculated using Eqs. (3)–(6) is uniform in the
whole range (and, moreover, these relative deviations do not exceed�10% for M1 and M3
and �7% for M2 and M4 alloys).
The MES models of iron aluminides – alloys M2 and M4 – exhibited a higher
sensitivity to the changes in the forming conditions (deformation scale and forming
temperature) compared to alloys M1 and M3 as demonstrated in Fig. 1. The cause for
different deformation behavior can be found in the origin of various phases after the
thermal history of each of the materials, i.e., in the presence and morphology of phases,
whose formation is connected with the presence of the additives used. Those phases
(which function as some obstacles) influence both recrystallization (by blocking the
movement of the grain boundaries) and proper deformation during rolling. In case of M3
alloy, stresses along the grain boundaries, densely occupied by heterogeneous phases,
initiate intercrystalline fracture.
Acknowledgment. The investigation was made in the framework of research plans MSM
6198910015 and MSM 4674788501 (Ministry of Education of the Czech Republic).
1. C. G. Mc Kamey, J. H. Devan, P. F. Tortoreili, and V. K. Sikka, “A review of recent
developments in Fe3Al-based alloys,” J. Mater. Res., 6, No. 8, 1779–1804 (1991).
2. www.fmmi.vsb.cz/model
3. P. Kratochvíl and I. Schindler, “Conditions for hot rolling of iron aluminide,” Adv. Eng.
Mater., 6, No. 5, 307–310 (2004).
4. N. N. Krejndlin, Reduction Calculation for Hot Rolling [in Russian], Metallurgizdat, Moscow
(1963).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 47

UDC 539.4
Analysis of Fracture Mechanisms and Surface Quality in Drilling of
Composite Materials
J. Sedláèek 1,a and A. Humár 1,b
1
Brno University of Technology, Faculty of Mechanical Engineering, Institute of Manufacturing
Technology, Brno, Czech Republic
a ysedla10@fme.vutbr.cz, b humar@fme.vutbr.cz
The aim of this work is to clarify the interaction mechanisms between the drilling tool and material.
Drilling tests were carried out on glass/polyester and carbon/epoxy composites using different twist
drills. The cutting tools and machined surfaces were examined by optical microscopy, scanning
microscopy and surface profilometry to study composite damage and tool wear. Among the defects
caused by drilling, delamination appears to be the most critical and may occurs at both the entrance
and exit planes. A prediction model of thrust force for drilling without delamination is proposed.
Keywords: composite materials, delamination, surface quality, drilling, tool wear.
Introduction. Machining of composite materials is a rather complex task owing to
its heterogeneity, heat sensitivity, and to the fact that reinforcements are extremely
abrasive. Drilling is a frequently practiced machining process in industry owing to the
need for component assembly in mechanical pieces and structures. On the other hand,
drilling of laminate composite materials is significantly affected by the tendency of these
materials to delaminate and the fibers to pull from the matrix under the action of
machining forces (thrust force and torque).
Delamination Analysis. Delamination occurs along the fiber direction and develops
in two phases: the chisel edge action phase and the cutting edge action phase. The first
phase begins when the thrust force of the chisel edge into the exit surface reaches a critical
value and ends when the chisel edge just penetrates the plate. By examining the
photographs of exit surfaces and finished workpieces, it was found that the chisel edge has
a strong effect on the formation of delamination. First a small bulge emerges in the
vicinity of the drilling axis and then it develops along the fiber direction of the exit
surface. When the bulge grows to a certain degree, the surface layer splits open, the chisel
edge penetrates and the second (cutting edge action) phase starts. The delamination
damage initiated in the first phase further develops due to the continuous pushing and
twisting of the cutting edge. The chisel edge cuts the workpiece material with a large
negative rake angle and generates over 50% of the thrust force. Thus the chisel edge plays
a key role [1].
Delamination Model for Push-Out at Exit. A simple model for predicting thrust
levels that will induce “push-out at exit” or “peel-up at entrance” delaminations has been
proposed [2–4]. The delaminated area is assumed to be circular, and uncut portion is
modeled as an isotropic circular plate clamped on its contour (Fig. 1). Drilling and fiber
directions are shown in Fig. 2. The equation of energy balance can by expressed as
follows, using the linear elastic fracture mechanics (assuming Mode I crack propagation)
GdA �FdX � dU,
(1)
where G is the energy release rate per unit area, dA is the increase in the area of
delamination crack, F is the thrust force, X is displacement of the drill, measured from
position at which delamination started, and U is the stored strain energy. Note that
© J. SEDLÁÈEK, A. HUMÁR, 2008
48 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

2
dA ��( a�da)( a�da) ��a�2 �ada,
(2)
where a is the radius of delamination. For a circular plate with clamped ends subjected to
a concentrated load, the stored strain energy U is
MX
U �
a
8�
2
2
, (3)
where M is flexural rigidity of plate under drill and is determined from thin plate theory
or also called Kirchhoff plate theory as follows
3
Eh
M �
2
12( 1�
) ,
�
where E is the modulus of elasticity and � is the Poisson’s ratio for isotropic materials.
The displacement X in Eqs. (1) and (3) is given by
2
(4)
Fa
X � , (5)
16� M
using a, F , and M according to [3]. After substitution of above-mentioned equations
into Eq. (1), the energy balance of systems can be written as
2 2 2 2
2G
a F
16 32 16
dX dU
F
da da
d Fa d F a F a
� � � � � � . (6)
da �Mda �M�M Hence, the critical thrust force for crack propagation (as function of the uncut
thickness h) in case of the unidirectional orthotropic fiber composites is expressed as
follows
F ( h) �� 32MG
��
A Ic
Analysis of Fracture Mechanisms and Surface Quality ...
Fig. 1 Fig. 2
Fig. 1. Delamination scheme: plate with clamped contour.
Fig. 2. Convention for drilling and fiber directions: arrow indicates the direction of tool rotation.
G cE
h
( ) .
8 I
2
31��
Note that E 2 is the modulus of elasticity across the fiber direction, � 21 is the minor
Poisson’s ratio, and GIc is the interlaminar critical energy release rate (crack driving
force) in Mode I loading.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 49
2 3
21
(7)

J. Sedláèek and A. Humár
Tool Wear and Its Effect on Delamination. Among the possible wear mechanisms,
which include adhesion, diffusion, oxidation, plastic deformation and brittle fracture, only
abrasion and sometimes adhesion are of significance for cutting of composites [5]. Glass
fiber-reinforced plastic (GFRP) made by pultrusion, (polyester matrix, 70% glass volume,
thickness 9.5 mm) and drills made from different cutting materials were used for the wear
tests.
The wear intensity of high-speed steel drills has been very high when drilling of
GFRP, as it was expected. The width of facet at the drill major flank reached value
VB � 1.33 mm (v c � 31.7 m/min, Fig. 3a) for non-coated drill and a value VB � 1.04 mm
(v c � 35.2 m/min, Fig. 3b) for coated drill, after about two minutes (102 s) of work time.
It is of interest that the wear of high-speed steel drill is very high along all the length of
the main cutting edge, even near of the centre of drill, where the cutting speed is very low.
This fact confirms the very high abrasive effect of glass fibers in the wear process of the
cutting tool when machining of GFRP. The values of torque have increased approximately
2.5 times in accordance with an increase of tool wear and the values of thrust force have
increased almost 7 times for about two minutes of tool operation.
a b c
Fig. 3. Tool wear of non-coated drill, v c � 31.7 m/min (a), coated drill, v c � 35.2 m/min (b), and
coated drill, v c � 56.5 m/min (c).
The wear of the coated solid carbide drill was stable at the value of VB � 0.12 mm
after the first stage of growing for a relatively short time. It stayed without any remarkable
changes for more than five minutes (317 s) of work, in spite of the fact, that this drill had
operated at a higher cutting speed (v c � 56.5 m/min, Fig. 3c) in comparison with
high-speed steel drills (v c � 31.7–35.2 m/min). It could be expected that the solid carbide
drill wear will not be increase considerably regardless of the operation time over the next
few minutes. The values of torque and thrust force especially are growing very slowly due
to the tool wear for the solid carbide drill.
a b c d e
Fig. 4. Dependence of delamination on tool wear for different: values of facet width at the drill
major flank VB: 0.12 (a), 0.26 (b), 0.39 (c), 0.60 (d), and 0.77 mm (e).
For any tool material type used, it is important to secure sharp cutting edge. When a
tool starts to lose its sharpness, it tends to pull and unwind fibers from the drilled parts
instead of cutting them. In addition, excessive tool wear causes increase of thrust force
and consequent delamination. Hence, the cutting tool must be changed before wear
occurs. The dependence of delamination on tool wear is shown in Fig. 4a–e. The
50 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Analysis of Fracture Mechanisms and Surface Quality ...
unidirectional reinforced carbon/epoxy laminate, fabricated by hand lay-up technique
from prepreg was used for test (total thickness 6 mm, thickness of one layer 0.15 mm).
The holes of 6 mm in diameter were drilled by high-speed steel drill (clearance angle
� f �13 �,
point angle 2� r �118�), cutting speed vc � 30.2 m/min, feed per revolution
f � 0.1 mm.
Surface Quality. The typical appearance of the drilled hole surfaces are shown in
Fig. 5a (along the fibers’ axes) and Fig. 5b (perpendicularly to the fibers axes) for the
GFRP drilling. The hole had been machined with a coated solid carbide drill of diameter
D� 10 mm at cutting speed vc � 56.5 m/min and feed per revolution f � 0.20 mm. The
hole axis is oriented horizontally in both of these figures. It is evident, that reinforcing
fibers fail by brittle fracture mechanism under tensile stress (Fig. 5a) and shear stress
(Fig. 5b). Close-up view of brittle fracture of glass fiber is shown in Fig. 5c. The bond
between fibers and matrix is damaged and a large amount of micro-particles is created
from fibers and matrix. Surface roughness is maximum when the fibers are loaded
compressively at 45� angle. With the convention of Fig. 2, where the arrow indicates the
direction of tool rotation, surface roughness is maximum at 135 and 315�, and in this
position the torque applied is maximum. The same observation was reported by other
investigators [2].
a b c
Fig. 5. Drilled hole surfaces: along (a) and perpendicularly (b) to the fibers’ axes and close-up view
of brittle fracture of glass fiber (c).
Conclusions. An analysis of delamination damage caused by thrust force (feed
force) of twist drill at the exit plane has been provided. The critical thrust force for crack
propagation is a function of uncut thickness h and material properties of machined
composite materials. To avoid delamination, the thrust force of drill should not exceed this
value. Hence, the feed rate should be reduced and usage of a drill with short chisel edge
and sharp cutting edge is recommended. The chisel edge generates over than 50% thrust
force, and worn drills with VB � 1.33 mm can increase thrust force by 7 times, as shown
experiment. The reinforcing fibers are the main reason of tool wear in drilling of
composites, particularly in case of high-speed steel drills. The surface roughness of drilled
holes is maximum when the fibers are loaded compressively at 45� angle.
1. H. Zhang, W. Chen, D. Chen, and L. Zhang, Key Eng. Mater., 196, 43–52 (2001).
2. S. Abrate, in: P. K. Mallick (Ed.), Composites Engineering Handbook, Ch. 15, Marcel Dekker
Inc. (1997).
3. M. Ozaki, Supervisory Control of Drilling of Composite Materials, University of California,
Berkeley.
4. H. Hocheng and C. C. Tsao, J. Mater. Proc. Technol., 140, 335–339 (2003).
5. G. Spur and U. Lachmund, in: S. Jahanmir, M Ramulu, and P. Koshy (Eds.), Machining of
Ceramics and Composites, Ch. 7, Marcel Dekker Inc. (1999).
Received 28. 06. 2007
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UDC 539. 4
Localization of Plastic Deformation and Fracture in Aluminum Polycrystals
N. V. Zarikovskaya 1,a and L. B. Zuev 2,b
1
Institute of Strength Physics and Materials Science, Siberian Branch of the Russian Academy of
Sciences, Tomsk, Russia
2
Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia
a chepko-znv@mail.ru, b lbz@ispms.tsc.ru
The effect of the grain size as a basic structural parameter on plastic strain macrolocalization has
been studied for polycrystalline aluminum. The mathematical form of the above dependence has
been verified. The limiting cases have been defined both for small- and coarse-grain ranges. The
effect of sample dimension on the macrolocalization period has been considered.
Keywords: plastic deformation localization, polycrystalline aluminum, deformation curve,
autowave, spatial period, failure.
Introduction. The plastic deformation of polycrystalline materials is an essential
and often a defining factor in many technological processes. At present significant
progress has been made in the physical theory of plasticity. A significant volume of
experimental data on the distinctive features of deformation and fracture has been
obtained for polycrystalline aluminum.
Plastic flow tends to localize at all the stages. The form of localization patterns
varies from the yield limit to fracture depending on the prevailing law of work hardening.
Our experimental investigations suggest that the observed regularities exhibited by
plastic flow are the result of self-organization of the deforming medium. According to
Zuev and Danilov [1], the above regularities can be considered as waves of localized
plastic deformation.
Experimental Procedure. The uniaxial tension tests were performed for a wide
range of mono- and polycrystals using an Instron-1185 testing machine with load F �
10 kN and loading rate � �� . � �
33 10 6 m/s.
Localized strain zones on the test specimen were revealed by the method of
double-exposure speckle interferometry [1], which yields distributions of plastic strain
tensor components [1].
Out of five types of deformation localization patterns only three are observed on the
flow curve of polycrystalline aluminum, namely:
� At the stage of linear work hardening a set of mobile nuclei of localized plastic
deformation originates in the test specimen and moves in a regular fashion, thereby
forming a running wave.
� At the stage of parabolic work hardening a set of immobile nuclei of deformation
localization emerges in the test specimen.
� At the pre-failure stage localized plastic deformation nuclei merge together,
resulting in necking and viscous failure of the test specimen.
The distribution patterns of plastic strain tensor components are shown �xx in Fig. 1
for polycrystalline aluminum both at the linear and the parabolic work hardening stage.
The observed regularities of plastic flow localization are common to all deforming
materials [1, 2]. It is found that plastic deformation tends to localize in certain zones of
the deforming specimen and is characterized by macroscopic scale, i.e., wavelength �.
It has been found that � depends on material parameters, i.e., length scale, crystal
lattice geometry, grain size, etc. Therefore, to determine the dependence of � on the grain
size and dimensions of a polycrystalline material is of particular interest.
© N. V. ZARIKOVSKAYA, L. B. ZUEV, 2008
52 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

� xx
t, s t, s
The tests were conducted using A85 aluminum samples whose grain size was easily
varied from 0.008 to 10 mm by the method of collective recrystallization.
Grain Size Dependence of Localization Wavelength for Polycrystalline
Aluminum. Figure 2 shows � as a function of the grain size D. Numerical processing of
the above dependence yields the following equation:
where a and b are the positive dimensional constants [3].
The solution to the above equation is as follows:
Localization of Plastic Deformation and Fracture ...
a b
Fig. 1. Space–time distributions of the elongation component obtained for polycrystalline aluminum
having a grain size D �190 �m: (a) linear stage at ��4.8–5.6%; (b) parabolic stage at
��8.0–8.8%.
d� dD�a��b� 2 , (1)
� 0
� �
1�Cexp( �aD)
, (2)
where � 0 � ab, and C is a non-dimensional integration constant.
Fig. 2. Wavelength � dependence on the grain size D for polycrystalline aluminum.
Equation (2) describes, with a sufficient accuracy, a set of experimental �( D) data
in a wide interval of D values (correlation coefficient R � 0.98). The curve in Fig. 2 may
be subdivided into three portions [3]: 1) as D goes up to 0.5 mm, � grows exponentially
up to �e aD (Fig. 3a); 2) in the range 0.5 �D�2.5 mm the dependence takes on the
logarithmic form ( � ln D ) (Fig. 3b); 3) at D� 2.5 mm, � becomes constant (�� �0�
15 mm).
� xx
L, mm L, mm
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N. V. Zarikovskaya and L. B. Zuev
a b
Fig. 3. Limiting cases of the wavelength dependence on grain size: (a) D � 0.5 mm; (b) D � 0.5 mm.
The effect of sample geometry (in particular, the sample thickness) on the macrolocalization
period was examined for aluminum samples having grain size D� 0.5 mm.
It can be seen in Fig. 4, with increasing sample thickness, � grows as well.
Numerical processing of experimental data yielded constants a� 1.1 mm �1 and
b� 0.2 m �2 for 2�10�50-mm samples and a� 1.5 mm �1 and b� 0.2 m �2 for
5�10�50-mm samples. Evidently, b is unaffected by the sample thickness.
Fig. 4. Grain size dependence of macrolocalization periods on the sample thickness: lines 1 and 2
correspond to t1 � 5 mm and t2 � 2 mm, respectively.
Distinctive Features of Deformation Macrolocalization at the Prefracture Stage.
In order to get a holistic picture of deformation for polycrystalline aluminum, the final
stage of the process, i.e., the prefracture stage, has been explored. It was shown earlier [4]
that the most striking feature of the plastic deformation localization reveals itself at the
latter stage.
The prefracture stage is a parabolic one, i.e., the stress–strain dependence for this
stage has the form � ~ �
n (where n is the parabola exponent). It has been shown that
with n� 0.5 the localized deformation nuclei move along the sample at a velocity V [4],
V( n) �V ( n�q) .
0
At the parabolic stage (n � 0.5) the localized deformation nuclei become motionless
(V � 0), while at the linear stage (n� 1) they move synchronously with different velocities.
The nuclei locations were plotted in the X()or t X ( �) coordinates, where X is the
nucleus’ coordinate, t is the deformation time, and � is the deformation (Fig. 5).
54 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
2
(3)

Fig. 5. Positions of localization nuclei vs. time.
Localization of Plastic Deformation and Fracture ...
It can be seen from the plot that with n� 0.4 the nuclei’s trajectories would form a
bundle whose pole pinpoints the location of future fracture.
The velocity of a nucleus can be defined from the slope of the straight line. Also, it
should be noted that the nuclei move with different velocities, some of them disappearing
altogether.
Thus, one can predict the place of future fracture long before the beginning of
visible necking.
1. L. B. Zuev and V. I. Danilov, Phil. Mag. A, 79, 43 (1999).
2. L. B. Zuev, Ann. Phys., 3, 965 (2001).
3. L. B. Zuev, B. S. Semukhin, and N. V. Zarikovskaya, Int. J. Solids Struct., 40, 941 (2003).
4. L. B. Zuev and V. I. Danilov, Tech. Phys., 50, 1636 (2005).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 55

UDC 539. 4
A Method for Low-Cycle Fatigue Life Assessment of Metallic Materials
under Multiaxial Loading
S. Shukaev, 1,a M. Gladskii, 1,b A. Zakhovaiko, 1,c and K. Panasovskii 1,d
1 National Technical University of Ukraine “Kiev Polytechnic Institute,” Institute of Mechanical
Engineering, Department of Machine Dynamic and Strength of Materials, Kiev, Ukraine
a shukayev@users.ntu-kpi.kiev.ua, b,d gladsky@gmail.com, c zakhov@users.ntu-kpi.kiev.ua
A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is
proposed, which is based on the modified Pisarenko–Lebedev criterion, the linear damage
accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests
of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given.
The tests were carried out at three Mises strain levels (0,6, 0,8, and 1,0%) with various
combinations of proportional and non-proportional strain paths. All the tests were carried out at
room temperature. The proposed method turned out to be effective and to allow for such factors as
strain state type, strain path type and loading irregularity.
Keywords: multiaxial low-cycle fatigue, irregular loading, titanium alloys, damage
accumulation, limit state criteria.
Introduction. Machine and construction elements often undergo irregular multiaxial
cycle loading. Though multiaxial fatigue of materials has been studied for a long time and
sufficient experimental data has been accumulated, the problem of including a loading
irregularity in a low-cycle fatigue area is still important. Numerous attempts to describe
fatigue damage process have been made, resulting in the development of a large number
of damage accumulation models.
The most generally employed is the linear damage accumulation concept proposed
by Miner, whereby damages D per cycle at a variable loading amplitude are added
linearly and the failure happens when D��ni N
i
fi �1,
where ni is the number of
one-level loading cycles and N fi is number of cycles to failure under a given loading
level. This approach is easy to use but it fails to give an adequate estimation of life in
many cases.
There have been many attempts to develop a model based on the nonlinear
accumulation of fatigue damage, but most of them disregarded the complex influence of
such factors as the stress state type, loading path, previous stress history in the process of
fatigue damage accumulation. Fatemi and Yang [1] have carried out a substantial survey
of the existing models, proposed a classification thereof, discussed advantages and
disadvantages of each model.
In the paper, the influence of sequential loading effects is studied on VÒ9 titanium
alloys under tension–compression, torsion and 90� out-of-phase non-proportional loading.
The life estimation method is proposed both for regular and irregular multiaxial loading.
A damage model is put forward, which considers the nonproportional effects arising at a
change of the loading regime.
Experimental Procedure. A high-temperature titanium alloy VT9 of the Ti–Al–Mo–
Zr–Si system belongs to two-phase (�� �)
martensitic alloys. The chemical composition
(in wt.%) of the material is given in Table 1. The microstructure of the material of the
specimen billets consists of (�� �)-phases
of equiaxial structure and corresponds to the
second type in the nine-type scale for bar materials according to Instruction No. 1054-76
of the All-Union Institute of Aircraft Materials.
© S. SHUKAEV, M. GLADSKII, A. ZAKHOVAIKO, K. PANASOVSKII, 2008
56 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Table 1
Chemical Composition of VT9 Alloy
Al Mo Si Fe Zr H2 N2 C
6.50 3.40 0.30 0.081 1.58 0.006 0.018 0.06
Specimens were made from as-delivered rolled bars 25 mm in diameter. The
mechanical properties of the material, which were determined by tensile testing of
125-mm-long solid cylindrical specimens at room temperature, have the following mean
values: proportional limit 758 MPa, yield strength 865 MPa, ultimate strength 973 MPa,
elongation 17%, reduction of the cross-sectional area 45%, and elastic modulus 118 GPa.
For the purpose of providing a stress-strain state close to a homogeneous one,
tubular specimens with an outer diameter of 11 mm, wall thickness of 0.5 mm, gauge
length of 20 mm were used. The realized strain paths are shown in Fig. 1.
a t o
Fig. 1. Schematics of strain paths used.
For the VT9 titanium alloy the test program as given in Table 2 was implemented.
The basic modes were as follows: tension–compression, alternating torsion, and 90�
out-of-phase loading. The first stage of the program was the block axial loading and/or
torsion moment test with given strain ranges. During this test the strain path remained
constant. The second stage of the program involved testing of the specimens with
changing of the strain path. A transition from one strain path to the other was conducted
when the D value reached 0.5 and then the specimen was cycled to failure. At the third
stage the test with a multiple strain path change was carried out.
Proposed Method. It was previously mentioned that the application of the
Pisarenko–Lebedev modified criterion for the fatigue life assessment of the VT1-0
titanium alloy under regular nonproportional loading shows a good agreement between
the predicted and test data due to the complex consideration of the strain state type and
nonproportionality of loading [3]. Therefore it is recommended to apply the Pisarenko–
Lebedev modified criterion as well as the chosen damage accumulation hypothesis for
assessing the VT9 titanium alloy fatigue life. In this study, the two damage accumulation
hypotheses were analyzed: the linear hypothesis and the Manson approach with the
Pisarenko–Lebedev equivalent strain in both cases, according to which the damage curve
is a nonlinear function of the relative fatigue life,
Di ni N fi q
� ( ) ,
A Method for Low-Cycle Fatigue Life Assessment ...
where q� ( N fi N fr ) � ; � is the material constant to be calculated from the test data for
sequential double-level loading, and N fr is the number of load cycles to failure at a
“reference” loading level.
Analyzing Figs. 2 and 3 one can see that during the application of the Pisarenko–
Lebedev modified criterion and the linear damage accumulation hypothesis the best
correlation between the predicted and test data is obtained for alternating torsion (paths
t_01 and t_02).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 57

S. Shukaev, M. Gladskii, A. Zakhovaiko, and K. Panasovskii
Table 2
Strain Peak Values and Number of Cycles to Failure for VT9 Titanium Alloy
Test type � a � a 3 n i N f
% cycle
a_01 a 0.8 – 157 293
a 1.0 – 136
a_02 a 1.0 – 98 245
a 0.8 – 147
a_03 a 0.6–0.8–1.0–0.8 – 50 519
a_04 a 1.0–0.8–0.6–0.8 – 50 491
oatota – 0.8 1.0 50 475
oa o 1.0 1.0 77 218
a 1.0 – 141
atat_1/5 a 1.0 – 40 423
t – 1.0 130
atat_1/3 a 1.0 – 65 510
t – 1.0 219
t_01 t – 0.8–1.0–1.2–1.0 50 601
t_02 t – 1.2–1.0–0.8–1.0 50 528
at a 1.0 – 97 398
t – 1.0 301
ta t – 1.0 398 603
a 1.0 – 205
ao a 1.0 – 98 184
o 1.0 1.0 86
to t – 1.0 282 390
o 1.0 1.0 108
ot o 1.0 1.0 80 384
t – 1.0 304
As a result, one can come to a conclusion about the linearity of damage accumulation
process for a given loading type. The combined application of the Pisarenko–Lebedev
modified criterion and of the Manson’s approach showed a high level of correlation
between the predicted data and test results for all the loading programs except the
alternating torsion. So, the following modification of the Manson approach is proposed:
�� ( )
Di � ( ni N fi ) ,
� �
�N
� �
� � � �
where �� ( ) ��
fi � 2 N
� � � � ��fi
1 � �,
�N
� � � � � � is the strain path orientation angle, which
fr � �N
fr � �
�
��
� �
determines the dominating type of the strain state, ��
� a fs
arctan � , �
��
� �,
� fs and � fs
a fs �
58 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
(1)

are the fatigue strength coefficients for a
finite life N f in the uniaxial and torsional
loading cases.
Thus, the damage accumulation during
the alternating torsion is linear, during the
tension–compression is calculated using the
Manson approach, and during the biaxial
proportional and non-proportional loading is
assessed by their linear interpolation.
The application of formula (1) resulted
in the best agreement between the predicted
and experimental data as shown in Fig. 4.
Conclusion. The proposed method of
fatigue life assessment under multiaxial lowcycle
regular and irregular loading, which is
based on the Pisarenko–Lebedev modified
criterion, the linear damage accumulation
hypothesis, and the nonlinear Manson
A Method for Low-Cycle Fatigue Life Assessment ...
Fig. 2 Fig. 3
Fig. 2. Comparison between the fatigue lives predicted by the modified linear damage rule and the
experimental fatigue lives.
Fig. 3. Comparison between the fatigue lives predicted by the modified damage curve approach and
the experimental fatigue lives.
Fig. 4. Comparison between the fatigue lives
predicted by the proposed approach and the
experimental fatigue lives.
approach proved to be effective and to allow for such factors as the strain state type, strain
path type, and loading irregularity.
1. A. Fatemi and L. Yang, “Cumulative fatigue damage and life prediction theories: a survey of
the state of the art for homogeneous materials,” Int. J. Fatigue, 20, No. 1, 9–34 (1998).
2. T. Itoh, M. Sakane, M. Ohnami, et al., “Dislocation structure and non-proportional hardening
of type 304 stainless steel,” in: Proc. of the 5th Int. Conf. on Biaxial-Multiaxial Fatigue and
Fracture, Cracow (1997), Vol. 1, pp. 189–206.
3. S. Shukaev, A. Zakhovaiko, M. Gladskii M., and K. Panasovskii, “Estimation of low-cycle
fatigue criteria under multiaxial loading,” Int. J. Reliab. Life Machin. Struct., 2, 127–135
(2004).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 59

UDC 539. 4
Hot-Cracking of High-Alloyed Steels Evaluated by Wedge Rolling Test
I. Schindler, 1,a P. Suchánek, 1 S. Rusz, 1 P. Kubeèka, 1 J. Sojka, 1 M. Heger, 1
M. Liška, 2,b and M. Hlisníkovský 3,c
1VŠB – Technical University of Ostrava, Ostrava, Czech Republic
2 VITKOVICE – Research & Development, Ltd., Ostrava, Czech Republic
3 TØINECKÉ �ELEZÁRNY, a.s., Tøinec-Staré Mìsto, Czech Republic
a ivo.schindler@vsb.cz, b miroslav.liska@vitkovice-vyzkum.cz, c marek.hlisnikovsky@trz.cz
We present a new methodology of determination of hot-cracking of metallic materials, which is
based on laboratory application of the wedge rolling test and computer processing of the results
obtained. The experiment was made with selected new types of high-alloyed free-cutting (ferritic
and austenitic) steels. The initial specimens underwent an additional modification enabling easier
development of cracks which consisted in milling out of the defined V-shaped notches on a side wall
of a specimen. After taking specimens from the rolled material, we performed the metallographic
analysis of microstructures by means of optical microscopy as well as a SEM analysis of the cracks.
The resulting microstructure in the propagating crack vicinity was markedly influenced by this
fracture. In the crack vicinity, a noticeable refinement of grains was observed due to the
stress-induced recrystallization and occurrence of deformation zones that were pronounced by the
rolled-out and stretched sulphides. As a rule, fractures were created by the ductile failure with
visible pits, caused by tearing of sulphides from the material. Susceptibility of the studied steels to
hot-cracking was evaluated and compared.
Keywords: hot-cracking, wedge rolling test, free-cutting stainless steel, microstructure.
Introduction. Based on the long-term research of plastic properties of metallic
materials, a new methodology of hot formability was developed on the basis of wedge
rolling test realized in laboratory conditions of the Institute of Modeling and Control of
Forming Processes at VŠB-TU Ostrava [1]. A simple laboratory test performed by rolling
of the wedge-shaped specimen on plain rolls provides a possibility of effective investigation
of hot deformation behavior of metallic materials, due to implementation of a wide range
of height reductions in a single specimen. The wedge rolling test is suitable for fast
evaluation of formability as well as, in combination with subsequent metallographic
analyses, for study of selected structural processes. Similarity of laboratory and industrial
rolling provides conditions for the appropriate quantitative comparison and application of
results in practice.
Laboratory Hot Rolling Conditions. The experiment was made with two selected
types of high-alloyed free-cutting stainless steels – the ferritic steel 17043STiMod (with
0.05 C, 0.30 Mn, 0.12 Si, 0.50 S, 16.4 Cr, 0.34 Ti in wt.%) and the austenitic steel
17247SCuTi (0.04 C, 0.23 Mn, 0.14 Si, 0.20 S, 1.41 Cu, 8.9 Ni, 17.0 Cr, 0.41 Ti). Initial
wedge specimens with trapezoid shape have the following dimensions: width 15 mm,
minimum thickness 3 mm, length 94–150 mm (depending on the predicted rolling forces),
and angle 434 � �. They underwent an additional modification enabling easier development
of cracks which consisted in milling out of the defined V-shaped notches on a side wall of
the specimen. The single-pass rolling of specimens in the laboratory mill stand K350 was
used, after heating directly to the forming temperature (i.e., 800–1100�C for the ferritic
steel, and 800–1250�C for the austenitic steel). The rolls with diameter of 140 mm rotated
at nominal speed of 110 min �1 , final thickness of the rolled specimens was 3.2 mm on
average.
© I. SCHINDLER, P. SUCHÁNEK, S. RUSZ, P. KUBEÈKA, J. SOJKA, M. HEGER, M. LIŠKA,
M. HLISNÍKOVSKÝ, 2008
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Immediately after rolling, each specimen was cooled down in a water bath with the
aim of fixing of the structure. Its plan was scanned to the form of bit maps which enabled
calculation of deformation and speed relations along the length of the rolled product [2].
The program KLIN [1] has been specially developed on the basis of computer image
analysis and gradual comparison of the total and partial volumes of the initial specimen
and the rolled product. The main advantage of the above program is that it can operate
with arbitrary irregular plan shape of the rolled product and take into account the
influence of uneven spread and changing thickness along the rolled product in the
calculation. Figure 1 illustrates the shape of the selected rolled specimen as well as the
calculated quantities.
Fig. 1. Plan shape of the rolled out wedge and strain/speed relations along the rolling stock
(austenitic steel, temperature 900�C).
Processing of Experimental Data. In case of the rolled products from the austenitic
steel, larger elongation can be observed, as compared to those from the ferritic steel,
whereas the latter exhibited larger spread. The steel 17247SCuTi was characterized by
relatively poor plastic properties – cracks occurred even at the highest forming temperature
T �1250�C. With decreasing rolling temperature frequency of cracks raised, which is
shown in Table 1 summarizing the achieved results and Fig. 2a.
Table 1
Occurrence of Cracks in Particular Rolled Out Specimens near Notches V1 to V8
Steel grade T ,�C V1 V2 V3 V4 V5 V6 V7 V8
17043STiMod 1100
1000
900
800 �
17247SCuTi 1250
1200
1100
1000
900
800
�
�
�
�
�
�
�
Hot-Cracking of High-Alloyed Steels ...
Note: � = an evident crack; � = absence of notch due to necessary shortening of the specimen.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 61
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�

I. Schindler, P. Suchánek, S. Rusz, et al.
a b
Fig. 2. Details of cracks after rolling of selected specimens: (a) austenitic steel rolled at 900�C –
notch V6; (b) ferritic steel rolled at 800�C – notch V5.
The steel 17043STiMod was characterized by much better plastic properties (Fig. 2b).
No cracks developed even at the highest forming temperature 1100�C. With decreasing
forming temperature the number of cracks initiated in the area of notches increased, but
differences observed at forming temperatures 800 to 1000�C are by no means considerable.
The flow of the material spread, appearance of side surfaces and character of cracks are
very different as compared with the investigated austenitic steel.
Structural and Fracture Analysis. Micrographs in Fig. 3 demonstrate shapes of
selected cracks under notches that were subjected to the largest deformation. Structure of
the specimens from steel 17043STiMod (Fig. 3a) is created purely by ferrite with
separated sulphidic inclusions. It is very probable that the main cracks were developed
under the material surface: they did not ascend to surface in the notch area. In the vicinity
of the crack, refinement of the structure is observed due to a higher deformation and
stress-induced recrystallization. The developed fractures were controlled by a mixed
(transcrystalline and intercrystalline) ductile fracture mechanism, which is illustrated by
Fig. 4a, b (rolling at 1000�C). Specimens from steel 17247SCuTi have an austenitic
structure with very high occurrence of large sulphidic inclusions. Evident deformation
zones are visible in the surroundings of the propagating crack, pronounced by deformed
and elongated sulphides (Fig. 3b). Fine cracks, perpendicular to the axis of the main crack,
occur again. The crack started obviously from the surface of the rolled product but with
proceeding deformation it was closed by influence of the material flow. The cracks were
created by a ductile fracture mechanism with large occurrence of pits caused by tearing of
sulphides from the material – see Fig. 4c, d (rolling at 800�C).
a b
Fig. 3. Metallographic photographs of cracks under last notches (the largest height reduction):
(a) ferritic steel rolled at 1000�C; (b) austenitic steel rolled at 800�C.
Conclusions. In this study of formability, the results of conventional plastometric
(e.g., torsion [3]) experiments exhibited high response of the studied material to varying
thermomechanical conditions of forming, but have often been burdened with data
scattering (mainly due to premature fracture of small specimens containing relatively large
defects). The wedge rolling test gives the results that can be evaluated in a more difficult
way and, in addition to that, it is suitable only for materials with impaired plasticity. In the
62 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

a b
Hot-Cracking of High-Alloyed Steels ...
c d
Fig. 4. Photographs from SEM – view of cracks under last notches (the largest height reduction).
case of most steel grades, it is necessary to improve its sensitivity by the milled notches,
which function like initiators of cracks in spreading parts of the rolled product.
As far as rollability is concerned (which is evaluated by a number of cracks, their
shape and location in the rolled products), it can be concluded that, in comparison with
similar tests performed with other types of steel, reduced formability was observed for
both free-cutting steels with sulphur, notwithstanding some differences in their deformation
behavior. The specimens from the ferritic steel 17043STiMod had better plastic properties
in comparison to the austenitic steel 17247SCuTi.
In the crack surroundings, a refinement of the structure was observed due to the
stress-induced recrystallization and occurrence of deformation zones that were pronounced
by the rolled-out and stretched sulphides. As a rule, fractures were created by a tough
failure with visible pits, caused by tearing of sulphides from the material containing high
level of detrimental sulphur.
Acknowledgments. The methodology of wedge rolling test has been developed under the
Research Plan MSM6198910015 (Ministry of Education of the Czech Republic). The tested
materials have been obtained in the framework of solution of the Project Impuls FI-IM 2/043
(Ministry of Industry of the Czech Republic).
1. M. Heger, I. Schindler, J. Franz, and K. Èmiel, in: CO-MAT-TECH 2003, STU Bratislava
(2003), p. 255.
2. P. Suchánek, I. Schindler, P. Turoòová, et al., in: Steel Strip 2006, Steel Strip Society (2006),
p. 349.
3. I. Schindler and J. Boøuta, Utilization Potentialities of the Torsion Plastometer, PS Katowice,
Poland (1998).
Received 28. 06. 2007
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 63

UDC 539. 4
On Mechanics of Deformation and Crushing Processes
L. Berka 1,a
1
Czech Technical University, Faculty of Civil Engineering, Department of Building Structures,
Prague, Czech Republic
a berka@fsv.cvut.cz
The mechanics of crushing and breaking of particles is one of the most intractable problems in
materials science. The stressed states of processed materials are significantly inhomogeneous, and
thus the deformation and disintegration mechanisms vary greatly. Two techniques have been
developed for realizing these processes as a quasi-homogeneous transition. The device and method
developed by Enikolopov transform a solid polymer spontaneously into powder. The same loading
system is now used for obtaining fine-grained metals, similarly as when using the ECAP device
developed by Valiev. Both techniques are now used for obtaining nanostructured materials. The
common feature of both types of methods is the formation of new physical surfaces. These are
particle-free oversurfaces or grain boundaries. The method requires a supply of energy in the form
of mechanical work, and this is mostly done by simultaneous action of pressure and shear stress.
The formation of free oversurfaces in stressed solid bodies is the subject of fracture mechanics. The
Griffith equation is employed to describe the problem.
Keywords: technology, processes, solids, crushing, mechanics, polar continuum, particle,
oversurface, grain, grain boundary.
Introduction. Granulation forms the basis of many mechanical technologies that
aim to change the material substructure into a bulk. Two techniques have been developed
for realizing these processes as a quasi-homogeneous transition [1, 2]. The device and
method developed by Enikolopov [3] transforms a solid polymer spontaneously into
powder. The same loading system is now used for obtaining fine-grained polycrystals,
similarly as when using the ECAP device [4] developed by Valiev. Both techniques are
now used for obtaining nanostructured materials [5]. It is necessary to clarify the
micromechanisms of these processes for the purposes of materials science as well as
practical applications.
The initial phase of the processes in question is the state with large deformations
where local rotation as a part of the deformation gradient cannot be neglected. This effect
has been studied experimentally using X-ray techniques [6, 7] and also microscopically on
the polished surface of specimens [8–10]. The theoretical analysis of deformations
assuming local rotations is known as the Cosserat continuum theory. This theory was
developed in the second half of the 20th century [11, 12]. A number of problems
involving formation of the substructure and grain size were solved using a coupled stress
theory [13, 14].
The second phase of the spontaneous fragmentation process of quasi-homogeneous
solids, which takes place under pressure and shear stress, results in the formation of new
physical surfaces, i.e., particle-free oversurfaces [3] and a new grain structure with new
grain boundaries [4]. The limit states of individual shear cracks and shear bands are now
under very intensive theoretical and experimental study. An early paper [15] provided an
elastic solution for the in-plane crack problem as well as the out-of-plane crack problem.
3D shear cracks were studied in [16–18] using the extended finite element method and
continuum-discontinuum modeling.
A description of the final state of the process now arises from the superposition of
the two phases. This shows the formation of the field of deformations and rotations and
shear spherical cracks that they induce. The deformation field around a spherical
© L. BERKA, 2008
64 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

macrocrack was studied in [19], using an interaction energy integral method. Attempts to
solve the above mentioned problems are based on the assumption of a homogeneous
continuum with individual defects [20, 21]. The aim of this paper is to put forward a
model of the granulation process, in which a quasi-homogeneous solid changes its grain
size and structure in the whole body volume.
A Model of the Granulation Process in a Solid Body. The general principle of an
idealized granulation process is a transition of a homogeneous solid body into a bulk of
homogeneous particles having surface tension and the same mass as in the original body.
The process is comparable with brittle fracture, but the stress states and crack modes are
different. Brittle fracture takes place mainly under tensile stress and in the form of the first
crack opening mode. According to the experimental results introduced above, the
analyzed process continues under the combination of both shear and pressure stresses.
This stress state then results in cracks of the 2nd and 3rd modes. The energy balance
principle used in the study of crack problems is expressed by the Griffith equation:
dE �dS �dU�dW �0, dW � 2 dU,
(1)
where E is the total potential energy of a cracked body, S is the surface energy of the
crack, U is the strain energy of a deformed body with a crack, and W is the potential
energy of the applied loads. The presented relation between W and U is valid on
condition that the strains are elastic.
The Polar Continuum Mechanics Equations. Deformations in technological
processes are always large and the experimental results introduced above show that in
theoretical description kinematic rotations of a deformed material cannot be neglected.
The effect of local rotation is described in the mechanics of deformable bodies by
micropolar continuum theories. There, the whole system of deformations (Fig. 1) and
stresses is supplemented by the introduction of the moment stress tensor � ij and
distortion tensor � ij into the equations that describe its mechanical behavior. The
deformation of the differential representative volume element of a material is expressed
by the following relations [11]:
dui �ui, jdxj ��ijdxj��ijxj, �ij �12( ui, j �u j, i ), �ij
�12(
u � u
� �� � , d� �� dx ��
dx .
i, j j, i
i ijk ij i i, j j ij j
On Mechanics of Deformation and Crushing Processes
Fig. 1. system of deformations [11].
The stresses � ij and m ij that occur in the centers of the volume element planes are
described by the following equations:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 65
),
(2)

L. Berka
� �0, � �� �� � �0
.
(3)
ij, j nm nm imn ij, j
The elastic behavior of isotropic materials is then defined by the following relations:
� � � 1
sij � 2G�
��ij ��
ij �, sij
� ( � ij ��ji ), ���ii ,
�1�2�
� 2
m
mij mji
� � �
aG
� �
( ), ,
2
4
2
ij
4aG�ij
�� ji �ij
where G and � are elastic constants and a and � are parameters of the material
substructure.
The strain energy dU in the differential volume element dV is determined by the
following formula:
dU �udV , u�s� �m�
.
(5)
ij ij ij ij
Spherical Shear Cracks in a Spatially Compressed Material. A crucial point in
the granulation process is connected with the origin of the spherical particle form. It is
necessary to take into account the continuous field of local rotations resulting from large
shear strain. Experimental results show that at a certain level of the shear strain, rotations
stay discontinuous [6]. When the material is assumed to be isotropic, the originating
discontinuities acquire the form of a sphere as these rotations are always spatial.
Furthermore, this transition is possible owing to the energy flux coming from the
compressed volume elements into the surface layers and originating along the spherical
discontinuities, which can be seen as frozen eddies with boundary layers. To reach the
conditions for the transition limit state, the Griffith equation is used. The quantities of the
surface energy S and strain potential energy U, therefore, have to be determined.
Let us now assume spherical shear cracks on the surface of a sphere placed inside a
representative volume element cube (Fig. 2). The cracks are bounded by circles, which
originate from sections parallel to the sides of the cube. Their surface area is the same
as that of the six spherical segments. The differentials of their surface area and volume are
determined by the following formulas:
2 3 3
dA �12�Rsin �d�, dV �6�Rsin
�d�, (6)
where R is the radius of the sphere and � is the angle between its normal and meridian
plane.
The crack surface energy dS is now obtained by multiplying the crack surface area
2dA by the specific surface energy �, which also contains the energy of the plastically
deformed surface layer.
ds �Rd� dh �dssin ��Rsin �
c�Rsin �
Fig. 2. Volume element cube.
66 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
(4)

The strain energy density u in the material with polar stresses is now calculated by
the substitution of inverse relation (4) for �ij in Eq. (5), and further arranged and
expressed in the form containing the invariants S () and M () of the stress and moment
tensors sij and mij :
�
sij sij � sii sjj
31 ( � �)
mij mij � �mij
mji
u�
�
2G 2 2
4aG( 1��)
�
� �
�
�
�
�
��
��
�
2
A S
1 S () 1
M 2 � M
D ( ) � ( 2)
S ( 2)
2G3( 1 �)
2
2aG( 1��
2 ) . (7)
The strain energy dU is now expressed using Eqs. (5)–(7)
S
M M
D
dU �
S
G � aG
�
�
�
�
�
��
��
�
� 2
� 1 () 1
� �
�
( 2)
2 3( 1 �)
2
��
2 ( 1��
A S
( 2) ( 2)
2
�
� 3 3
�R
sin �� d .
(8)
) ��
Substituting both quantities dS and dU in the Griffith equation, Eq. (1) results in
the following formula:
�
�
dE ��2�� ��
A S
S
M M
D
S
G � a
�
�
�
�
�
��
��
�
2
1 () 1
( 2) � � ( 2)
( 2)
2 3( 1 �)
2 2
2 G(
1�
� )
�
2 � 2
Rsin ��6�R sin � � 0.
(9)
��
An approximation is accepted for the purpose of simplifying the equation. The angle
� is assumed for the octahedral plane, i.e., the value of sin 2 � then equals 3/4. The
character of the parameters a and R should be pointed out. Both express the length and
stand for the characteristic dimension of structural elements, i.e., the particle size.
Therefore, an equation taking into account the condition R�a leads, after some
rearrangement, to the following quadratic form regarding the structural element size a:
S
2 2 1 D
a
S aG M
2
()
2
( 1�
) 3 2 16 ( 1 ) 3(
1�
�
�
�
�
��
� �
��
��
�
� �
�
On Mechanics of Deformation and Crushing Processes
A S
( ) ( 2)
M
�� ( 2)) �0
. (10)
The solution of this form will be the subject of the next theoretical and experimental
analyses.
Conclusions. The solution of the problem under study is based on the account of the
mutual coupling of shear deformations with local rotations. The rotations predetermine the
origin of shear spherical cracks in all internal points of the macrovolume of the material.
The energy supplied to the system by the applied spherical pressure then leads, together
with other physicochemical auxiliary effects, to new conditions for thermo- dynamic
equilibrium of the process and to the formation of new physical surfaces.
Acknowledgment. The author appreciates the support of GA ASCR for the project No.
IAA200710604.
1. V. V. Boldyrev and K. Tkáèová, J. Mater. Synth. Proc., 8, 121–132 (2000).
2. J. R. Kolobov and R. Z. Valiev, in: NAUKA, Novosibirsk (2001), p. 228.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 67

L. Berka
3. N. S. Enikolopian, Macromolec. Chem., 185, 1371–1381 (1984).
4. R. Z. Valiev, A. V. Korznikov, and R. R. Milyukov, Mater. Sci. Eng., A186, 141 (1993).
5. G. Wilde et al., Mater. Sci. Eng., A449-A451, 825–828 (2007).
6. B. M. Rovinskij and V. M. Sinajskij, Some Problems of Strength of Solids, Moscow (1958).
7. W. Diepolder,V. Mannl, and H. Lippman, Int. J. Plasticity, 7, No. 4, 313–328 (1991).
8. L. Berka, J. Mater. Sci., 19, No. 5, 1486–1495 (1982).
9. L. Berka, Proc. ICM 8, Univ. of Victoria B. C. (1992), Vol. I, pp. 160–164.
10. L. Berka, et al., Solid Mech. Appl., 135, 235–246 (2006).
11. R. D. Mindlin and H. F. Tiersten, Arch. Rat. Mech. Anal., 11, 415 (1962).
12. A. C. Eringen, in: H. Liebowitz (Ed.), Fracture, Academic Press (1968), Vol. II, pp. 621–729.
13. R. S. Lakes, in: H. Mühlhaus and J. Wiley (Eds.), Continuum Model for Materials with
Microstructure (1995), pp. 1–22.
14. H. C. Parks and R. S. Lakes, Int. J. Solids Struct., 23, No. 4, 485–503 (1987).
15. G. I. Barenblatt and G. P. Cherepanov, J. Appl. Math. Mech., 25, 1654–1666 (1961).
16. G. C. Sih and H. Liebowitz, in: H. Liebowitz (Ed.), Fracture, Academic Press (1968), Vol. II,
pp. 151–166.
17. N. Moes, A. Gravouil, and T. Belytschko, Int. J. Num. Meth., 2549–2568 (2002).
18. E. Samaniego and T. Belytschko, Int. J. Num. Meth., 62, 1857–1872 (2002).
19. M. Gosz and B. Moran, Eng. Fract. Mech., 69, 299–319 (2002).
20. S. Casolo, Int. J. Solids Struct., 43, 475–496 (2006).
21. E. Z. Wang and N. G. Shrive, Eng. Fract. Mech., 52, No. 6, 1107–1126 (1995).
Received 28. 06. 2007
68 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539.4
Area and Point Approaches in Fatigue Life Evaluation under Combined
Bending and Torsion Loading
A. Karolczuk 1,a and E. Macha 1,b
1 Opole University of Technology, Opole, Poland
a A.Karolczuk@po.opole.pl, b E.Macha@po.opole.pl
We present a new nonlocal approach to nonuniform stress distribution, consisting in reduction of
stresses to representative local ones in the critical plane for fatigue life calculation. The shear and
normal stresses are averaged in two overlapping areas of different sizes on the critical plane. The
proposed method is compared with the point (in critical distance) method and both are verified by
fatigue tests under combined bending and torsion. Verification is done for the experimental and
calculated fatigue lives with use of two multiaxial fatigue failure criteria.
Keywords: nonlocal approach, critical plane approach, stress gradient.
Introduction. Geometry or loading features of components often causes the
formation of nonuniform stress/strain distribution. In case of fatigue loading, cracks are
formed under the influence of a stress/strain which undergo changes in time and in some
volume of the material. This complicated process must be taken into account in the proper
fatigue life estimation.
On the basis of experimental evidences concerning the stress gradient effect on
fatigue life, the following phenomena have been revealed: (i) under equal nominal
stresses, fatigue lives of specimens subjected to reversed bending are higher than fatigue
lives of the same specimens subjected to reversed push-pull loading [1, 2]; (ii) the
initiation of nonpropagating fatigue cracks under loading close to the fatigue limit for
defective materials [3, 4]; (iii) low influence of shear stress gradient on fatigue lives for
specimens subjected to reversed torsion [1, 5].
The main goal of the present paper is to develop a model of reduction of nonuniform
stress distributions around a hot spot in a material to representative local stresses.
Representative means taking the above-mentioned (i, ii, iii) phenomena into consideration.
The phenomenon (i) allows for the averaging of stresses in some critical space of the
material. Fundamental issue is to define the shape and size of this critical space.
Definition of these geometrical features is dictated by the other phenomena – (ii) and (iii).
The phenomenon (ii) accounts for too small opening stresses active at a small distance
from the stress concentrator. Therefore, it is postulated that an averaged value of normal
(opening) stresses over the potential crack growth plane, provided that the crack growth
must reach the critical value. The phenomenon (iii) is associated only with the
macroscopic shear stress gradient which arises, e.g., from torsion of the cylindrical
specimens. At the observation scale of a few metallic grains, the macroscopic shear stress
gradient is insignificant and has no influence on the crack initiation and especially on the
crack growth. However, in the case of a significant shear stress gradient at the mesoscopic
scale, which arises, for instance, from notches or defects with sizes of a few metallic
grains, it is necessary to take this effect into account during an early crack formation
phase. This effect should be considered in the area where crack is formed in the maximum
shear stress plane (stage I). The size of this area depends mainly on the material state and
loading (type and test conditions) but for most cases this area is very small in comparison
to the area where cracks grow on the maximum normal stress plane (stage II).
The paper outlines the model of shear and normal stresses reduction over the critical
areas. A new approach is verified using the test results on hour-glass shaped specimens
© A. KAROLCZUK, E. MACHA, 2008
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 69

A. Karolczuk and E. Macha
subjected to combined cyclic bending and torsion. Moreover, the point approach (the
theory of critical distance), which has been analyzed and developed by Taylor and Susmel
[6], has been also verified.
Fatigue Tests. Hour-glass shaped specimens made of 18G2A steel (Table 1), with a
minimum diameter of 6.5 mm, were subjected to sinusoidal combinations of plane
bending and torsion under different moment amplitude ratios � M � Mt, a Mb,
a (torque/
bending) and two phase shifts �� 0 and ��� 2 (Mb() t � Mb, a sin( 2�ft), Mt t ()�
Mta , sin( 2�f��), f � 20 Hz). Failure of a specimen is defined by about 30% drop in
bending rigidity. The specimens were cut from a 15.8-mm-diameter drawn bar, machineturned
and conventionally polished with progressively finer emery papers.
Table 1
Torsion: � � � ( N�N ) / 1
a af f
The Area Method. The proposed area method for reduction of nonuniform
distributions of shear and normal stresses to the uniform ones takes into account the
phenomena (i), (ii), and (iii) as mentioned above. It is believed that the crack growth or
fatigue damage is a local process. It means that the crack initiation period can be
described also by the crack growth process. A crack grows from a size of one or a few
grains up to the size which defines the component failure. During this process, the crack
growth could be governed by different mechanisms (Mode I, Mode II, etc.). Under the
conventional uniaxial fatigue tests, the crack grows through the material over the plane
which originally had a uniform stress distribution. In the case of fatigue tests with the
stress gradient effect, a crack grows over a nonuniformly stressed plane. The local stresses
which vary over the potential crack growth plane have an influence on the local crack
growth rate and consequently on the total fatigue life. To avoid the complicated process of
iterative modeling of the crack growth using the finite element method, it is assumed that
the averaged stresses over the potential fracture plane reflect the stress gradient effect.
Since the shear crack growing process (stage I) is usually limited to the area of a few
grains, the averaging process of shear stresses � ns is restricted to that area. The tensile
crack growth (stage II) which usually leads to the final failure takes place in the area
which defines failure by its size or by the beginning of an unstable crack growth rate. Two
components of the stress tensor are distinguished for the averaging process, i.e., shear � ns
and normal � n . The plane orientation whereby these components are determined is
defined by multiaxial fatigue failure criterion and is well known as the critical plane. The
averaged stresses over two overlapping areas Ans, c and Anc , are calculated according to
the following relations:
�� 1 ��
�� ns ( tns , , ) � � �ns ( tns , , , �,
rdA ) ns ,
A
ns, c Ans
Cyclic Properties of the 18G2A Steel
m�
Push-pull: � � � ( N�N ) / 1
a af f
� 1 �
�� n (, tn)
� � �n(, tn, �,
rdA ) n ,
A
nc , An
where � n is the normal vector to the critical plane, � s is the shear vector on the critical
plane, �, r are the local coordinates on the critical plane, and t is time. The averaged
stresses �� ns and �� n which are functions of time and the critical plane orientation are
70 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
m�
� � ( � K�)
/ 1
�af , MPa m� N � , cycles �af , MPa m� N � , cycles K �,
MPa n�
157 9.5 198 10 6
. � 204 8.2 124 10 6
. � 1323 0.207
Indices: af = fatigue limit, a = amplitude, p = plastic, � = torsion, � = push-pull, N = cycles.
a p
a
n�
(1)

introduced into the multiaxial fatigue failure criterion. Because the analyzed data pertain
to the macroscopic stress gradient, the averaging process over the area of a few grains is
not necessary. Only the normal stresses � n are averaged over the area Anc , . For
simplicity, the shape of the Anc , area is assumed to be semicircular. The failure of the
specimens is defined by about 30% drops in bending rigidity. It means that the averaging
process in the cross section of the specimen may be reduced to the semicircular-shaped
area of 4.17 mm 2 and this value is taken as Anc , .
The Point Method. This method assumes that the stressed state, at some critical
distance from the hot spot, is responsible for the material failure. If the equivalent stress at
this point is high enough, then the crack will propagate and cause the final failure.
Results and Discussion. Stress and strain histories at an arbitrary point (x, y) of the
specimen cross section were computed from bending Mb ()and t torque Mt t ()moments
by means of a kinematic hardening model as proposed by Mroz and modified by Garud.
More details can be found in [7].
Two multiaxial fatigue failure criteria have been verified using test results. One of
them is the well known Matake criterion [8],
� � � af
N
��ns,
a ��� �
� �� n,max �af
� � � �
af �
N
�
2 1
�
�
�
for which the critical plane orientation coincides with the maximum shear stress
amplitude. The other criterion is based on two parameters,
� �
�
Ncalc � N �
��
���
af
n,max
m�
�
�
�
�
,
�
calc
1/ m� �
�
�
�
� �
�
Ncalc � N �
��
���
The final fatigue life N calc
�
is determined by the minimum fatigue life between N calc and
�
N calc ; �� n,max is the maximum value in time of the averaged normal stress �� n () t on a
plane where this stress reaches its maximum, �� ns, a is the amplitude of the averaged shear
stress �� ns () t on a plane where this stress is maximum. Figure 1 gives the results obtained
by the proposed area method.
a b
Area and Point Approaches in Fatigue Life Evaluation ...
Fig. 1. Comparison of the experimental and calculated fatigue lives: the area method and (a) Matake
criterion, (b) two-parameter criterion. [Dashed lines represent the maximum experimental scatter
band �3.1 and � �� ( L�0) � ( L�0
). ]
�
xz , a zz , a
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 71
af
ns, a
,
m�
�
�
�
�
.
(2)
(3)

A. Karolczuk and E. Macha
The following error parameters were applied for the evaluation of the criteria and
methods:
() i
k
() i N calc
1 () i
E � log , E E
() i m � � ,
N
k
exp
i�1
(4)
k
1 () i 2
2 2
Estd
� �(
E � Em)
, Ex � Em�Estd ,
k�1
i�1
where k is a number of specimens (k � 43).
Different critical distances L were examined in the case of the point method. The
best results used for the Matake criterion were obtained for L� 1.35 mm (Fig. 2a) and for
the two-parameter criterion for L� 0.8 mm (Fig. 2b).
a b
Fig. 2. Comparison of the experimental and calculated fatigue lives: the point method and (a) Matake
criterion, (b) two-parameter criterion. [Dashed lines represent the maximum experimental scatter
band �3.1 and � � ( L) � ( L).]
� � xz , a zz , a
Conclusions. Under the investigated test conditions, the experimental and calculated
fatigue lives can be successfully correlated with the two-parameter multiaxial fatigue
failure criterion based on the critical plane approach and the proposed area method for
nonuniform stress reduction. The proposed area method takes into account the different
effects of shear and normal stress gradients on the fatigue life. The classical point method
neglects this effect, but the results obtained by this method are only a little worse.
1. I. V. Papadopoulos and V. P. Panoskaltsis, Eng. Fract. Mech., 55, No. 4, 513 (1996).
2. F. Morel and T. Palin-Luc, Fatigue Fract. Eng. Mater. Struct., 25, 649 (2002).
3. Y. Murakami and M. Endo, Int. J. Fatigue, 16, 163 (1994).
4. M. Endo and I. Ishimoto, Int. J. Fatigue, 28, 592 (2006).
5. D. McClaflin and A. Fatemi, Int. J. Fatigue, 26, 773 (2004).
6. L. Susmel and D. Taylor, Int. J. Fatigue, 28, 417 (2006).
7. A. Karolczuk, Eng. Fract. Mech., 73, 1629 (2006).
8. T. Matake, Bull. JSME, 20 (141), 257 (1977).
Received 28. 06. 2007
72 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539. 4
Comparison of Fatigue Criteria for Combined Bending–Torsion Loading of
Nitrided and Virgin Specimens
Š. Major, 1,a J. Papuga, 2,b J. Horníková, 1,c and J. Pokluda 1,d
1 Brno University of Technology, Brno, Czech Republic
2 Czech Technical University, Prague, Czech Republic
a ymajor02@stud.fme.vutbr.cz, b papuga@pragtic.com, c hornikova@fme.vutbr.cz,
d pokluda@fme.vutbr.cz
This work deals with fatigue life of plasma-nitrided and virgin specimens made of a low-alloy high
strength steel. Specimens were subjected to an in-phase combined bending–torsion loading. The
plasma-nitrided specimens exhibited a significantly improved fatigue resistance. The criterion
proposed by McDiarmid was found to be the most precise in the fatigue life prediction for virgin
specimens. On the other hand, the Matake criterion was the most successful for nitrided specimens.
Keywords: fatigue life, bending-torsion, nitrided layer, high-strength steel.
Motivation of the Research. Many new stress-based multiaxial criteria have been
proposed in recent years [1–4]. However, there is still significant lack of their experimental
verification. In order to partially fill this gap, in-phase combined bending–torsion
experiments were performed using specimens made of a low-alloy high-strength steel
(virgin specimens). Similar experiments were carried out on specimens containing surface
nitrided layers (nitrided specimens). An extended comparison between classical and
advanced multiaxial criteria as well as fatigue life of virgin and nitrided specimens was
performed.
Multiaxial Criteria. More than ten classical and advanced multiaxial criteria were
utilized to predict the fatigue life under combined bending–torsion. The complete set of
criteria can be found elsewhere [2]. Hereafter, only some of them will be mentioned in
more detail.
The most general form of fatigue criteria can be given as the inequality
af ( C ) �bg( N ) � f�1
,
(1)
where a and b parameters are set from two uniaxial fatigue limits (e.g., the fatigue limit
in the fully reversed torsion t �1 and in the fully reversed push-pull f �1 ). The linear
combination of shear (C) and normal (N) stresses in Eq. (1) can be also replaced by a
quadratic version. If the load data on the left-hand side (LHS) of Eq. (1) correspond to an
experimentally determined fatigue limit, the ideal state of equality should be achieved.
The fatigue index error I represents the degree of deviation from the ideal equality,
I �[( LHS�RHS) RHS] �100
%.
(2)
The ideal prediction leads to LHS� RHS,
i.e., I � 0. If I � 0, the criterion yields
conservative results since it predicts the failure of the specimen (component) under lower
loads.
Criteria proposed by McDiarmid, Matake, and Spagnoli can be considered as
classical ones. The McDiarmid criterion can be written as
C
t
N max
� �1
,
2S
(3)
a
AB , u
© Š. MAJOR, J. PAPUGA, J. HORNÍKOVÁ, J. POKLUDA, 2008
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 73

Š. Major, J. Papuga, J. Horníková, and J. Pokluda
where S u is the ultimate strength. The subscript a means the amplitude and the subscript
max denotes the maximum stress value. The shear fatigue strength t AB , for case A or
case B cracking (parallel to the surface or inwards from the surface, respectively). The
relation tAB , t � �1 is generally fulfilled for plane bending combined with torsion [5–6].
The Matake criterion can be expressed by the relation
�Ca, MSSR �( 2��) N max, MSSR � f�1
.
(4)
In this equation the fatigue limit ratio �� f�1 t�1
. The subscript MSSR means the
critical plane set according to the Maximum Shear Stress Range criterion.
As an example of the quadratic form, the Spagnoli criterion [7] can be mentioned,
�
2 2 2
Ca�N max � f�1.
(5)
The criteria put forward by Papadopoulos (integral approach) [8] and Goncalves et
al. [9] are examples of advanced approaches. In the Papadopoulos criterion the input
variables (the shear stress and the normal stress) are integrated over all planes,
5�
8�
2
2�
�
2�
2
� � � ( Ta( �� , , �)) d�sin ��� d d �( 3�3�) �H,max�
f�1
,
2
��0
��0
��0
where T a is the amplitude of resolved stress, �, �, and � are the Euler angles, and
� H ,max is a maximum value of the hydrostatic stress.
The Goncalves criterion is expressed as
5
��� � �
�
�
1
3
�di,max�
f
21 ( 1 3)
3�1 i�1
1 �1
where the parameters d i can be determined from minimum and maximum values of the
transformed deviatoric stress tensor
d �05 . (max s ( t) �min
s ( t)).
i i i
Experimental Procedure. The specimens were made of the high-strength low-alloy
steel ÈSN 41 5340. The basic mechanical properties of the material are � y � 805 MPa
and S u � 930 MPa. One of the surface treatment methods improving the fatigue life is the
deposition of nitriding layers by a plasma discharge [10]. The nitriding process parameters
are shown in Table 1. The experiments were made by means of the multiaxial-test
machine MZGS-100 at room temperature. The applied loading of frequency 29 Hz
comprised symmetric (R ��1) sinusoidal bending and torsion and their in-phase
combination.
Table 1
Step Temperature
(�C)
Nitriding Process Parameters
Wall
(�C)
N2/H2
Compression
(Pa)
74 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
,
U , V Pulse
(�s)
Time
(h)
Refining 510 460 20/2 70 800 100 –
Nitriding 515 455 21/7 260 530 120 32
(6)
(7)

Comparison of Fatigue Criteria ...
Table 2
The Average Iav and Absolute Average Iabs , av Values of Error Indices
Criterion Specimens virgin nitrided
Indices (%) Iabs, av Iav Iabs, av
Dang Van 7.35 �3.03 8.45 �0.35
Crossland 7.28 �5.42 8.65 �2.47
Sines 11.85 �11.23 12.32 12.82
McDiarmid, Eq. (3) 7.08 �3.02 8.65 1.72
Findley 7.08 �3.38 8.62 �0.87
Matake, Eq. (4) 7.12 �3.04 8.32 �0.23
Spagnoli, Eq. (5) 10.50 4.33 8.56 3.35
Papadopoulos (integral approach), Eq. (6) 7.36 �3.04 8.46 �0.35
Papadopoulos (critical plane) 11.08 �6.30 16.56 �6.70
Goncalves et al., Eq. (7) 8.62 4.14 13.92 5.20
Fig. 1. The constant life diagram (n � �
510 5 cycles) according to the McDiarmid criterion for virgin
and plasma-nitrided specimen.
Conclusions. Our results show that the fatigue life of the nitrided specimens is
significantly higher than that of the virgin specimens. The curves are plotted using the
McDiarmid criterion for the number of cycles n�510 �
5 and the experimental data
correspond to the fatigue life of ( 5 2) 10 5
� � . This conclusion can be made even though a
relatively small number of investigated nitrided specimens were tested. The calculated
error indices reveal that the McDiarmid criterion was the most successful in the fatigue
life prediction for virgin specimen and the Matake criterion was the most successful for
nitrided ones.
Acknowledgments. This research was supported by the Czech Science Foundation under the
Project No. GA106/05/0550 and the Ministry of Education and Youth of the Czech Republic under
the Research Plan MSM 0021630518.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 75
I av

Š. Major, J. Papuga, J. Horníková, and J. Pokluda
1. D. F. Socie and G. B. Marquis, Multiaxial Fatigue, Warrendale (2000).
2. J. Papuga, Mapping of Fatigue Damages, PhD Thesis, Czech Technical University in Prague,
Prague (2005).
3. I. V. Papadopoulos, P. Davoli, P. Gorla, et al., Int. J. Fatigue, 19, No. 3, 219–235 (1997).
4. I. V. Papadopoulos, Int. J. Fatigue, 16, 377–384 (1994).
5. D. L. McDiarmid, Fatigue Fract. Eng. Mater. Struct., 14, No. 4, 429–453 (1991).
6. D. L. McDiarmid, Fatigue Fract. Eng. Mater. Struct., 17, No. 12, 1475–1484 (1994).
7. A. Carpinteri and A. Spagnoli, Int. J. Fatigue, 23, 135–145 (2001).
8. I. V. Papadopoulos, Fatigue Fract. Eng. Mater. Struct., 21, 269–285 (1998).
9. C. A. Gonçalves, J. A. Araujo, and E. N. Mamiya, Int. J. Fatigue, 27, 177–187 (2005).
10. J. Pokluda, I. Dvoøák, Š. Major, and H. Horáková, in: W. S. Johnson (Ed.), Fatigue 06,
Elsevier (2006).
Received 28. 06. 2007
76 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539. 4
Quantitative Fractographic Analysis of Impact Fracture Surfaces of Steel
R73
L. Mrázková 1,a and H. Lauschmann 1,b
1
Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of
Materials, Prague, Czech Republic
a Linda.Mrazkova@fjfi.cvut.cz, b Lausch@kmat.fjfi.cvut.cz
Macroscopic images of fracture surfaces of Charpy test specimens of steel R73 were studied, where
bright spots in images represent cleavage facets or ductile dimples, respectively, both in special
orientations. Within image analysis, they may be taken for the most significant textural element.
Being the brightest patches in the image, they can be extracted by thresholding. Their counts and
area distribution are closely related to temperature and impact energy.
Keywords: Charpy test, fractography, image analysis.
Introduction. Textural fractography as a part of quantitative fractography investigates
fracture surfaces as image texture. Many types of textural elements can be replaced by
simple binary objects which are representative for the given type of fracture. In this study,
macroscopic images of fracture surfaces obtained from Charpy tests are analyzed. Bright
spots were chosen as typical textural elements of these fracture images. Statistical
characteristics of counts and areas of them are discussed.
Experimental. Within the scope of research thesis [1], the Charpy impact tests of 20
Charpy V-notch (CVN) specimens were performed. Experimental material was low-alloy
steel R73. Its chemical composition (in %) and mechanical properties are listed in Table 1.
Microstructure of R73 steel is a ferrite-pearlite mixture.
Table 1
Chemical Composition and Basic Mechanical Properties of Steel R73
Chemical composition Mechanical properties
C Mn Si P S Cu Cr Yield strength (MPa) 394
0.51 0.75 0.3 0.012 0.009 0.08 0.24 Ultimate tensile strength (MPa) 732
Ni O H Mo V N AlC Elongation (%) 22.8
0.16 1.8 1.2 0.04 0.003 0.0053 0.023 Contraction (%) 42.4
Impact energy was measured on instrumented impact pendulum device Roell Amsler
RKP 450. The nominal energy of the machine was 300 J, angle of the fall 150� and
striking velocity at the impact point 5.23 m/s. Temperatures of the specimen ranged from
�70�Cto230�C. Figure 1 shows measured values of notch toughness (impact energy
divided by the area of specimen cross section under V-notch). Transition temperature
determined as the inflection point of transition curve is 44�C.
Fracture surfaces of all specimens contain transgranular cleavage facets. Their
number decreases, and simultaneously the area of ductile fracture increases with increasing
impact energy [1].
From the point of view of application, the upper bound of transition area is
especially important. It is located at about 90�C. Above this temperature, the material
possesses its full notch toughness of about 70 J/cm 2 .
©L.MRÁZKOVÁ, H. LAUSCHMANN, 2008
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L. Mrázková and H. Lauschmann
Fig. 1. Transition curve of R73 steel.
Image Analysis and Results. Macroscopic images of the fracture surfaces were
provided by means of digital camera. All images were done under the same light
conditions. Examples of images of the surfaces created under different temperatures are
shown in Fig. 2. The images were cropped for demand of image analysis – only the
fracture surfaces were analyzed.
a b
Fig. 2. Fracture surfaces from Charpy test under temperature �10�C (a) and 70�C (b).
Images of fracture surfaces contain bright spots reflecting especially cleavage facets
[2], but also some of ductile dimples, both in certain ranges of orientation, so that they
reflect light into the camera lens. The area ratio of bright spots decreases with increasing
temperature of specimen. Consequently, analysis was focused on these bright spots which
can be considered as textural elements. Segmentation (selection of bright elements) was
accomplished by binarization by means of the same threshold value for all images. Output
of the binarization is on Fig. 3. These binary images provide data for further statistical
analysis.
a b
Fig. 3. Binary images of fracture surfaces obtained by thresholding. Fracture surface of specimen at
temperature �10�C (a) and 70�C (b).
78 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Two basic quantities of bright spots were measured: their number and their areas.
Various statistical characteristics of these quantities were estimated. Strong dependence on
notch toughness, as well as temperature has the area ratio of bright spots (total area of
bright spots/area of image), which is shown in Fig. 4. The data were fitted with parametric
function
�t�T�
p� A�Btanh � �,
A, B, C, T�const
,
(1)
� C �
where p determines the ratio of bright spots, t stands for temperature or notch
toughness, and A, B, C, and T are regression parameters. The Matlab function
fminsearch was used to estimate regression parameters by means of minimization of
variation.
a b
Quantitative Fractographic Analysis ...
Fig. 4. Dependence of bright spots’ area ratio on temperature (a) and notch toughness (b).
The area ratio of bright spots does not follow the transition curve (Fig.1) in the total
range. The width of transition area is smaller – the decrease starts at about 30�C. On the
contrary, indicating full toughness at about 90�C shows a tight agreement with the
transition curve.
Other characteristics with even better resolution of this limit are average and
standard deviation of bright spot areas (Figs. 5 and 6).
a b
Fig. 5. Dependence of mean area of bright spots on temperature (a) and notch toughness (b).
Values of the mean and standard deviation of bright spots area are divided into two
groups, representing fracture surfaces with and without cleavage facets, respectively. In
other words, in the second case, bright spots reflect only ductile dimples in a certain range
of orientations. Within individual groups, there are only small differences, while each
group has significantly different average value. The limiting point determines the
temperature of full toughness, 90�C, with high resolution.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 79

L. Mrázková and H. Lauschmann
a b
Fig. 6. Dependence of standard deviation of bright spots area on temperature (a) and notch
toughness (b).
Conclusions. Simple binary representation of textural elements in fractographs may
offer valuable quantitative characteristics of fracture surface. Bright spots in images of
fractures created within Charpy V-notch toughness testing were analyzed. Basic statistical
characteristics of their counts and areas were found to be determinative especially for the
temperature limit of full notch toughness of the material tested.
Acknowledgment. This research has been supported by the Ministry of Education of the
Czech Republic, research project “Diagnostics of materials” No. MSM 6840770021.
1. Š. Válek, Physical Mechanisms of Ductile-to-Brittle in Low-Alloy Steels [in Czech], Research
Thesis, FNSPE CUT, Prague (2005).
2. Š. Válek and P. Haušild, “Influence of microstructure on fracture energy of low-alloy steels,”
in: Proc. of Workshop 2006, CTU, Prague (2006), Vol. 2, pp. 360–361.
Received 28. 06. 2007
80 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539. 4
Microstural Features of Failure Surfaces and Low-Temperature Mechanical
Properties of Ti–6Al–4V ELI Ultra-Fine Grained Alloy
E. D. Tabachnikova, 1,a A. V. Podolskiy, 1,b V. Z. Bengus, 1,c S. N. Smirnov, 1,d
K. Csach, 2,e J. Miškuf, 2 L. R. Saitova, 3 I. P. Semenova, 3,f and R. Z. Valiev 3,g
1
Verkin Institute for Low Temperature Physics & Engineering, National Academy of Sciences of
Ukraine, Kharkov, Ukraine
2 Institute of Experimental Physics, Academy of Sciences of Slovakia, Kosice, Slovakia
3 Institute of Physics of Advanced Materials, USATU, Ufa, Russia
a tabachnikova@ilt.kharkov.ua, b podolskiy@ilt.kharkov.ua, c bengus@ilt.kharkov.ua,
d smirnov@ilt.kharkov.ua, e csach@saske.sk, f semenova-ip@mail.ru, g rzvaliev@mail.rb.ru
Microstructural regularities of failure surfaces and low-temperature mechanical characteristics in
quasistatic uniaxial tension and compression have been studied for ultra-fine grained structural
states of Ti–6Al–4V ELI alloy processed by equal channel angular pressing. Values of the yield
stress and uniform strain at 300, 77, and 4.2 K have been compared for structural states of the
Ti–6Al–4V ELI alloy that differ in the average grain size and the morphology of � and � phases.
Statistical distributions of dimple sizes on the failure surfaces have been studied for different
structural states and temperatures.
Keywords: equal channel angular pressing, mechanical properties, low temperatures.
Experimental Materials and Procedures. The investigations have been carried out
using Ti–6Al–4V ELI polycrystalline rods for medical applications (Intrinsic Devices
Company, USA), and their composition was (wt.%): Ti = base, 6.0 Al; 4.2 V; 0.2 Fe;
0.001 C; 0.11 O; 0.0025 N; 0.002 H.
Mechanical characteristics have been studied in uniaxial tension and compression
�4 �1
with a 410 � s strain rate using a stiff straining machine at 300, 77, and 4.2 K. The
specimens for tension had a 5.5 mm gauge length and a square cross section of
0.75�2.4 mm. Specimens for compression were rectangular prisms 2�2�7 mm.
The yield stress � 02 . , ultimate strength � u , uniform plastic strain �u (plastic strain
prior to the neck formation in the case of tension), and the strain to failure � f have been
measured from stress–strain curves.
The type of failure has been specified, and the failure surface morphology has been
studied with a TESLA BS-300 scanning electron microscope (SEM).
Three structural states of the Ti–6Al–4V ELI alloy have been investigated:
State 1: initial polycrystalline alloy with approximately 12% of � phase, � grains
have elongated shape with averaged sizes of 5–10 and 20–25 �m, respectively, � phase
in the initial microstructure forms an interlayer between � grains.
State 2: billets 40 mm in diameter and 150 mm long were processed at 600�C by four
ECAP passes with a 90� rotation around the billet axis in a die-set with a channel
intersection angle of 120�. After the equal channel angular pressing (ECAP), the average
grain size in the � phase is 0.5–1.0 �m. The quantity of the � phase decreases after the
ECAP from 12 to 8%. Colonies of twins are a very important feature of this state. Their
thickness is between 50 to 100 nm and the length is comparable with the average grain
sizes (0.5 and 1.0 �m) [1].
State 3: thermal treatment of initial polycrystalline rods was carried out. Billets 40 mm
in diameter and 150 mm long were heated up to 950�C, quenched in water, and further
aged. Then, the billet was processed at 600�C by four ECAP passes, which was followed by
© E. D. TABACHNIKOVA, A. V. PODOLSKIY, V. Z. BENGUS, S. N. SMIRNOV, K. CSACH, J. MIŠKUF,
L. R. SAITOVA, I. P. SEMENOVA, R. Z. VALIEV, 2008
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E. D. Tabachnikova, A. V. Podolskiy, V. Z. Bengus, et al.
multi-cycle extrusion at 300�C. This has resulted in a highly dispersed structure (� phase
fragments ranged from 200 to 400 nm) [1]. The volume fraction of the � phase was 5%.
Mechanical Characteristics of Ti–6Al–4V ELI Alloy. The averaged values of the
yield stress � 02 . , the ultimate strength � u , the uniform plastic strain �u , and the strain to
failure � f for all structural states of the Ti–6Al–4V ELI alloy tested in tension and
compression at 300, 77, and 4.2 K are listed in Table 1.
Table 1
Mechanical Characteristics of Ti–6Al–4V ELI Alloy in the Initial Coarse-Grained State 1
and Ultra-Fine Grained States 2 and 3 under Tension and Compression
Temperature
(K)
Structural
state
�02 . ,
GPa
� u ,
GPa
Tension Compression
�u � f �02 . ,
GPa
� u ,
GPa
300 State 1 0.80 0.91 0.10 0.17
State 2 0.98 1.03 0.04 0.07 1.10 1.28 0.13
State 3 1.23 1.30 0.04 0.08
77 State 1 0.99 1.08 0.15 0.19
State 2 1.49 1.57 0.03 0.06 1.58 1.63 0.02
State 3 1.76 1.90 0.03 0.07
4.2 State 1 1.59 1.66 0.06 0.06
State 2 1.69 1.84 2.14 0.06
State 3 1.50
The grain structure modification and the decrease in the grain sizes through the
ECAP processing lead to a considerable increase in the alloy yield stress � 02 . .Inthe
ultra-fine grained state 2 the yield stress increases by 22.5% at 300 K and by 50% at 77 K
as compared to the initial coarse-grained state 1. Heat treatment before the ECAP and the
extrusion stimulate a further decrease of the grain size (state 3) and result in an additional
increment of the yield stress � 02 . in comparison with state 2 (25.5% at 300 K and 18% at
77 K).
The difference in the � 02 . values in compression and tension (the so-called SD
effect) is observed for state 2 and its value is 12% at 300 K and 6% at 77 K.
The change of the structural state from 1 to 2 has led to a decrease of the uniform
plastic strain �u from 10 to 4% at 300 K, and from 15 to 3% at 77 K as it is shown in
Table 1. In state 3, the uniform strain �u practically coincides with the value obtained for
state 2 at 300 and 77 K.
At 4.2 K all specimens in states 2 and 3 fractured without macroscopic plastic
deformation. Only failure stress values are listed in Table 1 for these cases.
Analysis of Failure Surfaces. Failure surfaces of specimens in states 1 and 2, which
were tested under uniaxial tension at 300, 77, and 4.2 K, are oriented at an angle of 45°
(shear failure), as well as 90� (normal failure) with respect to the tensile axis. In state 3,
failure of specimens at 77 and 4.2 K took place only along different shear planes oriented
at an angle of 45� to the tensile axis.
It is important to note that only ductile failure and typical dimple failure morphology
were observed under uniaxial tension for all structural states of the specimens, which had
been deformed at 300, 77, and 4.2 K. A typical morphology of the failure surfaces is
shown in Fig. 1a and 1b. As one can see, the surfaces of shear failure have the dimple
pattern that is elongated in the direction of the shear crack propagation (Fig. 1a), while the
surfaces of “normal failure” have no elongation of the dimple pattern (Fig. 1b).
82 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
� f

Microstural Features of Failure Surfaces and ...
a b
Fig. 1. Failure surfaces of the Ti–6Al–4V ELI alloy subjected to tension at 77 K: (a) state 2: “shear
failure”; (b) state 2: “normal failure”; SEM.
It is of interest to study the dependence of the dimple size on the structural state of
the specimens as well as on the temperature of the experiment. Distributions of the dimple
sizes on the failure surfaces have been obtained for the normal failure as well as for the
shear failure at 300, 77, and 4.2 K for all three structural states studied. Examples of
typical dimple size distributions for 77 K are shown in Fig. 2.
Fig. 2. Typical dimple size distributions as observed on the normal and shear failure surfaces of the
Ti–6Al–4V ELI alloy after deformation at 77 K.
The distributions of the dimple sizes are not uniform for all cases studied. Table 2
contains average values of dimple sizes for all temperatures and structural states
investigated.
Analysis of the obtained dimple size distributions can be summarized as follows:
(i) the obtained dimple size distributions have a small dependence on the experiment
temperature;
(ii) transition from state 1 to states 2 and 3 leads to a decrease in the average dimple
sizes;
(iii) dimple size distributions change their shape at transition from state 1 to states 2
and 3 and become more sharp;
(iv) the maximum of the dimple size distribution is considerably higher for states 2
and 3 in comparison with state 1.
It is noteworthy that the observed increase in the height of the dimple distribution
maximum can be associated with differences in the distributions of structural inhomogeneities
of these states. Thus, a wider distribution of grain sizes has been observed in structural
state 1 (5–25 �m) as compared with states 2 (0.5–1.0 �m) and 3 (0.2–0.4 �m).
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E. D. Tabachnikova, A. V. Podolskiy, V. Z. Bengus, et al.
Table 2
Average Dimple Size Values for All Investigated Structural States of the Ti–6Al–4V ELI Alloy
Temperature
(K)
Average dimple size
Normal failure Shear failure
State 1 State 2 State 3 State 1 State 2
d ~20�m d ~ 07 . �m d ~ 03 . �m d ~20�m d ~ 07 . �m
300 3.3 1.9 2.0 4.3 2.7 2.3
77 4.3 2.7 4.6 2.9 2.7
4.2 4.5 2.7 3.8 2.6 3.1
State 3
d ~ 03 . �m
Discussion of Results. The observed increase in the yield stress � 02 . and decrease
of the uniform strain �u in state 2 as compared with state 1 of the Ti–6Al–4V ELI alloy
are explained by the presence of additional strong barriers for the dislocation slip in the
form of grain boundaries and twin colonies in state 2. Further 20% increase in � 02 . in
state 3, as compared with state 2, is apparently associated with a decrease in the average
grain size that leads to an increase in the specific grain boundary area that represents an
effective barrier for dislocations.
It is noteworthy that uniform strain values for states 2 and 3 practically coincide at
300 K, as well as at 77 K. Such behavior can be explained by a rather similar character of
microstructures: colonies of twins in state 2 and boundaries of � grains in state 3 can be
considered naturally as strong barriers for dislocation slip. Dislocation pile-ups that are
formed in front of such barriers can stimulate microcrack nucleation. This may explain the
presence of small plastic deformations in states 2 and 3 at 300 and 77 K.
Failure of specimens at 4.2 K in states 2 and 3 took place without macroscopic
plastic deformation, but only ductile shear fracture was observed on the failure surfaces of
those specimens. So, in this case, plastic deformation is localized and took place only in
the region of the fracture crack.
The SD effect observed for ultra-fine grained state 2 of Ti–6Al–4V ELI alloy can be
explained by the influence of pressure on the dislocation sources. And the difference in
tension/compression local pressures increases with decreasing grain size [2].
It is known from the literature [3] that the typical dimple size on the failure surface
of coarse-grained materials does not exceed the grain size, and the distribution of dimples
on the failure surface frequently has a maximum, which corresponds to the typical size of
the grain substructure [3]. Similar behavior is observed in the present work for state 1
(Fig. 2). But for ultra-fine grained states 2 and 3 the dimple size maximum exceeds
considerably the grain sizes, and the grain boundary is not an effective barrier for dimple
growth. Such effect was observed in nanocrystalline materials [4, 5], and it can be caused
by the process of “clustering” (grouping of several adjacent grains during plastic
deformation of nanocrystals) [4, 5]. And the size of such clusters in our case can be the
characteristic structural size that corresponds to the dimple size distribution maximum.
1. I. P. Semenova., L. R. Saitova, G. I. Raab, et al., Mater. Sci. Forum, 503-504, 757–762
(2006).
2. S. Cheng, J. A. Spencer, and W. W. Milligan, “Strength and tension/compression asymmetry
in nanostructured and ultrafine-grain metals,” Acta Mater., 51, 4505–4518 (2003).
3. V. I. Betekhtin and A. G. Kadomtsev, Phys. Solid State, 47, 825–831 (2005).
4. A. Hasnaoui, H. Van Swygenhoven, and P. M. Derlet, Science, 300, 1550 (2003).
5. H. Li, F. Ebrahimi, H. Choo, and P. K. Liaw, J. Mater. Sci., 41, 7636–7642 (2006).
Received 28. 06. 2007
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UDC 539. 4
Influence of Nitriding on the Fatigue Behavior and Fracture Micromechanisms
of Nodular Cast Iron
R. Koneèná, 1,a G. Nicoletto, 2,b V. Majerová, 1 and P. Baicchi 2
1 Department of Materials Engineering, University of �ilina, �ilina, Slovakia
2 Department of Industrial Engineering, University of Parma, Parma, Italy
a aradomila.konecna@fstroj.uniza.sk, b bgianni.nicoletto@unipr.it
Surface modification processes are increasingly used to fully exploit material potential in fatigue
critical applications because fatigue strength is sensitive to surface conditions. Nitriding is
extensively adopted with ferrous materials because it forms a hard and strong surface layer and a
system of superficial compressive residual stresses. Fatigue, however, is strongly dependent also on
defects and inhomogeneity. When nitriding is applied to nodular cast iron (NCI), the relatively thin
hardened layer (about 300 �m) contains graphite nodules (diameter of the order of 30 �m), casting
defects and a heterogeneous matrix structure. The paper presents and discusses the influence of
nitriding on the fatigue response and fracture mechanisms of NCI. A ferritic NCI and a synthetic
melt with different content of effective ferrite were initially gas-nitrided. Then, (i) structural analysis
of nitrided layers, (ii) fatigue testing with rotating bending specimens, and (iii) fatigue fracture
surface inspection were performed. Performance and scatter in fatigue performance is discussed by
selective inspection of fracture surfaces and identification fracture micromechanisms. A semiempirical
model explains observed trends in test results and is used for the process optimization.
Keywords: nodular cast iron, nitriding, fatigue, fracture mechanisms.
Introduction. NCI is a construction material with a wide range of applications in
engineering practice [1]. For fatigue-critical application the surface characteristics of NCI
may be modified by thermochemical surface treatments, such as nitriding, with formation
of a hard and strong surface layer and of a system of compressive residual stress. In
nitriding, N is diffused into the metal and such diffusion, once individual atoms of N have
penetrated the surface, continues as long as the temperature is high enough, and there is a
fresh supply of nascent N on the surface. A surface exposed to a nitriding medium will
generally form two distinct layers. The outside layer is called white (compound) layer and
its thickness generally ranges between zero and 25 �m (i.e., phases: �-Fe2-3N) [2]. Phase
��-Fe4N is known to show a plastic response particularly in comparison with brittle
microstructure containing both ����phases. Underneath the white layer there is a
diffusion zone (i.e., phase: ��-Fe4N) [2]. The properties of these layers depend on the type
of basic material and its original pre-process hardness. NCI is a widely used construction
material in the fabrication of severely stressed mechanical parts of complex geometry
because it combines a cost-effective casting technology with high fatigue strength [3].
Materials and Experimental Procedures. Two NCI were considered: (i) standard
EN-GJS 400 melt with ferritic matrix (see norm EN 1564) and (ii) the synthetic melt C
produced with addition of SiC into the liquid metal with different content of effective
ferrite (EF). The chemical composition of both melts was similar to approximately
eutectic composition. Two sets of smooth fatigue specimens were prepared from the
material under study. Then, one set of specimens of each material was subjected to a
nitriding treatment. The patented Nitreg ® Controlled Potential process was used on GJS
400, while melt C was subjected to optimized gas-nitriding treatment. The fatigue curves
were obtained on a rotating bending testing machine operating at 50 Hz with load ratio
R ��1. The fatigue limit � c was determined according to a reduced staircase method [4].
© R. KONEÈNÁ, G. NICOLETTO, V. MAJEROVÁ, P. BAICCHI, 2008
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R. Koneèná, G. Nicoletto, V. Majerová, and P. Baicchi
For melt C only two stress amplitude levels were investigated to assess the fatigue curve
trend. The fatigue fracture surfaces were investigated in SEM on selected specimens. The
fatigue initiation location and the mechanisms of stable crack propagation were sought.
Nitrided specimens tested at the same stress level and showing different fatigue lives were
selected to identify possible sources of weakness in case of both types of material.
Structural Characterization and Fatigue Behavior. The structure of GJS 400 was
characterized by ferritic matrix with a regular distribution of graphite nodules with size
ranging from 15 to 60 �m. A significant discontinuous network of carbides with
microshrinks on the boundaries of eutectic cells was observed, too. The matrix of melt C
was not homogeneous, with significantly different content of EF in each specimen. The
EF content for specimens with almost fully ferritic matrix is from 70 to 86%, for
ferritic-pearlitic matrix from 52 to 69% and for pearlitic-ferritic matrix from 41 to 51%.
The graphite nodules were observed in fully or not fully globular shape predominately
with size ranging from 30 to 60 �m and with small ratio of size ranging from 60 to 120 �m.
A nitrided layer of both materials is formed by a thin white layer on the surface of
specimen, diffusion zone and subdiffusion zones. The white layers were continuous with
variable thickness from 10 to 28 �m for GJS 400, respectively from 9 to 33 �m for melt
C, with local presence of graphite particles. A thicker white layer and diffusion zone were
identified in areas where graphite particles were present. In both materials a thin dark
layer, which is most probably a carbonitrided layer, in white layer was identified, when a
high magnification was applied. The nitrided layer of specimen 3 (GJS 400) was without
presence of cracks but in case of specimen 4 (short life, see Fig. 1), short cracks initiated
on the surface of specimens in white layer were observed. Therefore, from local structural
and EDS analyses it appears that in the specimen 4, in comparison with specimen 3, a
high concentration of nitrogen on the ferrite grain boundaries was locally found.
The fatigue curves of the untreated
and nitrided GJS 400 are shown in Fig 1.
The fatigue limit is � c � 169 MPa for
untreated and � c � 381 MPa for nitrided
NCI. The nitriding treatment has provided
a very significant improvement of the
fatigue response, confirming the range of
improvement determined by previous
tests on steels [3]. The high fatigue
strength is not exclusively due to the
formation of the hardened surface layer,
because favorable compressive residual
stresses are also produced in the surface
Fig. 1. Fatigue curves.
layers by nitriding. The fatigue life data of
the nitrided NCI are fitted with two
parallel fatigue curves, A and B, because
specimens subjected to the same applied stress amplitude showed fatigue lives differing
by more than two orders of magnitude. The trend of fatigue curves of melt C (Fig. 1)
showed higher number of cycles to failure for the same applied stress amplitude for
untreated melt C because of the lower EF. The fatigue data of untreated and nitrided
specimens of melt C showed no significant dependence of number of cycles to the failure
on content of EF. The trend of fatigue curve for nitrided specimens was found in between
the two parallel lines characterizing nitrided GJS 400, see Fig. 1. Vickers nanohardness
measurements of nitrided layers are presented in Fig. 2. The curves demonstrate longer
fatigue life of nitrided specimens having lower DHV values.
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Influence of Nitriding on the Fatigue Behavior ...
Fig. 2. Nanohardness measurements of the nitrided layer.
Fatigue Fracture Surfaces. From inspection of SEM macrofractographs, multiple
sites of fatigue crack initiation were confirmed by the presence of radial stairs on the
fracture surfaces. Cracks initiated at casting defects (microshrinks) were found below the
white layer, see Fig. 3a, while no crack initiation occurred at internal graphite particles.
Initiated cracks then propagated in two directions.
Transcrystalline cleavage characterized the growth through the white layer to the
surface (Fig. 3a). The fatigue crack propagation into the material was characterized
initially by local plastic deformation of ferrite around graphite nodule. Then crack
continued in diffusion and subdiffusion zone first predominantly by intercrystalline
decohesion along boundaries of ferrite grains (Fig. 3a) and then by formation of fine
striations (Fig. 3b). The presence of striations supports plastic deformation mechanisms of
ferrite. In the region of final static failure of both specimens, the crack propagated by
transcrystalline ductile fracture of ferrite with dimple morphology.
a b
Fig. 3. Fatigue fracture surface of nitrided NCI: interface white layer and diffusion zone (a) and
fatigue region with striations (b).
Interpretation for Fatigue Life of NCI in the Case of Nitriding. The scheme of
Fig. 4 summarizes (i) the current understanding of the parameters involved in controlling
fatigue crack initiation and fatigue life of rotating bending fatigue experiments, (ii) the
material features affecting fatigue life determined in this study, and (iii) the fatigue crack
paths.
Local stresses vary as shown with � b , which is fully reversed stress amplitude. It
gradually decreases because it is associated to the bending loading from maximum value
on the surface. Residual stress distribution � rs is not known exactly but based on
evidence in nitrided steels the compressive maximum stress (i.e., 200–300 MPa) is
expected near the surface and goes to zero at the case/core interface. This introduces a
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R. Koneèná, G. Nicoletto, V. Majerová, and P. Baicchi
positive mean stress effect that decrease with depth from the surface. Finally, from the
nanohardness curves of Fig. 2, the local material strength � h is expected to be maximum
near the surface (below the white layer) and to decrease to the core (base) strength.
a b
Fig. 4. Scheme of stress and strength profiles in the nitrided NCI and idealized microstructures and
crack paths for short fatigue life (a) and long fatigue life (b).
The NCI microstructure is schematically represented by eutectic cells in Fig. 4. Each
cell contains one graphite nodule. Cells are divided in several ferrite grains. Figure 4
shows two alternative schemes representative of two mechanisms observed at short and
long lives, respectively (specimens 3 and 4 in Fig. 1) in NCI having different content of
carbides and microshrinks at eutectic cell boundaries. Upon nitriding, the white layer can
be cracked, when the process is not optimized (Fig. 4a), or sound and compact (Fig. 4b).
In the first case cracks in the white layer propagate into the base material along the ferrite
grain boundaries. When the white layer is sound and compact, crack initiation takes place
at microshrinks below the surface at eutectic cell boundaries. Early fatigue crack
propagation is intercrystalline in the nitrided layer in both cases. In material with higher
content of nitrides at ferrite grain boundaries (specimen 4) the stable crack propagation is
shorter due to more brittle fracture behavior.
Conclusions. This study has investigated the influence of a nitriding treatment on
the material structure and on the fatigue response of nodular cast irons. Tests on smooth
specimens of nitrided nodular cast irons demonstrated a significant increase in the long
life fatigue strength after nitriding due to the formation of a hardened surface layer and a
compressive residual stress system. Nitrided specimens with longer fatigue lives showed
N content without scatter and lower DHV values. Fatigue crack initiation in the nitrided
specimens occurred at microshrinks below the white layer. Fatigue cracks propagated in
the diffusion and subdiffusion zone along ferrite grain boundaries where the content of N
and the nanohardness DHV were high.
Acknowledgments. This work was done as a part of the SK/IT project No10/NT and a part of
the VEGA grant No.1/3194/06. It is also consistent with the objectives of MATMEC, one of
Emilia-Romagna newly established regional net-laboratories (http:// www.matmec.it/).
1. J. Davis, Cast Irons/Metallurgy and Properties of Ductile Cast Irons, ASM Specialty
Handbook, The Materials Information Society, USA (1996).
2. A. Sinha, Physical Metallurgy Handbook, McGraw-Hill, New York (2003).
3. G. Nicoletto, A. Tucci, and L. Esposito, Wear, 197, 38 (1996).
4. O. Bokùvka, G. Nicoletto, L. Kunz, et al., Low and High Frequency Fatigue Testing,
CETRA, EDIS, �ilina (2002).
Received 28. 06. 2007
88 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539. 4
Microstructure and Fracture Morphology of Thermally Sprayed Refractory
Metals and Ceramics
O. Kováøík 1,a and J. Siegl 1
1 Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering,
Department of Materials, Prague, Czech Republic
a kovon@seznam.cz
The microstructural characteristics such as porosity, splat morphology and grain size of thermally
sprayed coatings made of both ceramic and refractory metals are investigated. Al2O3 and Cr2O3
coatings represent ceramic materials while pure W and Mo coatings represent the refractory
metals. The used deposition technology (RF-plasma, gas stabilized or water stabilized DC plasma)
was found to influence the coatings microstructure to a great extent by providing different particle
impact velocities and temperatures. At the same time the substrate temperature plays an important
role as is shown for refractory metal coatings deposited at different substrate temperatures.
Generally, all investigated coatings contained intrasplat cracks, intersplat pores and voids, individual
splats of different degree of deformation and different degree of intersplat sintering, crystal grains
formed inside individual splats or extending through many of them. It is shown that the size and
abundance of the above-mentioned microstructural features predetermine the fracture morphology
of the coating as well as mechanical properties.
Keywords: thermal spraying, refractory materials, microstructure, fractography, elastic
modulus.
Introduction. The increasing demands for sophisticated construction parts with
increased corrosion and heat resistance lead to the increased use of protective coatings.
Refractory materials fulfill the demands for corrosion, thermal, wear and fatigue resistance
and, when applied as coatings, help to preserve the low weight and mechanical properties
of the substrate material. A great advantage of protective coatings is the possibility to
renew the part by replacing any worn coating.
We discuss deposit properties of several thermally sprayed coatings of engineering
importance sprayed by three different techniques. The spray technology and process
parameters used are selected for each feedstock in order to provide favorable particle state
for the deposition based on previous experiments [1–3].
Experimental. Refractory ceramics Al2O3 and Cr2O3 were deposited on flat 4 mm
thick mild steel substrates by WSP ® PAL 160 water stabilized plasma torch at IPP, CAS,
Czech Republic. Tungsten deposits were prepared on thick stainless steel substrates by
Tekna PL-50 RF-ICP torch in an inert atmosphere at CREPE Sherbrooke, Quebec,
Canada. Molybdenum coatings were prepared on flat 4 mm thick mild steel substrates by
APS DC plasma torch Metco 3MB at CTSR, Stony Brooke, NY, USA. Spray conditions
are listed in Table 1. All substrates were grit-blasted before spraying.
The in-flight particle properties were measured using DPV-2000 instrument. The
elastic modulus of the Mo coatings was measured by four-point bending tests as described
in [4]. Moduli of other deposits were estimated from resonance frequency of the coating
beam. The total deposit porosity (open and closed) was estimated by weighting a sample
of the known volume using a precision scale.
Metallographic specimens for structure observations were prepared by electrolytic
polishing and etching. The splat thickness was measured by image analysis on a
polished/etched cross-section and the value is an average of approximately 200
measurements.
©O.KOVÁØÍK, J. SIEGL, 2008
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O. Kováøík and J. Siegl
Table 1
Feedstock Spray
technology
The Most Important Deposition Process Parameters
T s ,
�C
q c ,
slpm*
q p ,
slpm
q s ,
slpm
feed
rate,
g/mm
Results and Discussion. The measured in-flight temperature data ensure proper
melting of the feedstock powders and limited feedstock evaporation (see Table 1). The
impact velocity of the Mo particles was much higher than that of the W particles (see
Table 1) resulting in thinner splats (Table 2). Elastic moduli (Table 2) of the coating
ranges from 4 to 44% of bulk material modulus, both extreme cases were obtained for the
W deposits sprayed under the same conditions, but different T s . The deposit porosity �
(see Table 2) ranges from 2% to 33% with the lowest porosity achieved for W and highest
for Al2O3.
The results obtained clearly show the importance of the substrate temperature on the
deposit properties. The micrographs in Fig. 1 reveal two types of the deposit structure. For
the Mo deposits and the tungsten deposit at 290�C, the intersplat porosity contributes
significantly to the total porosity. On the other hand, the W deposits at 430�C (Fig. 1) and
560�C (not included on Fig. 1) show intersplat boundaries but only a limited number of
intersplat pores. In the case of W, the steep increase of elastic modulus between 290 and
430�C was detected (Fig. 2), suggesting the transition temperature (change from splash-
90 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
P,
kW
T p ,
�C
v p ,
�C
d mean ,
�m
W RF/ICP 560 6.3 (He) 30 (Ar) 100 (Ar) +
15 (H2)
40 80 4120** 40** 61**
W RF/ICP 430 6.3 (He) 30 (Ar) 100 (Ar) +
15 (H2)
40 80 4120** 40** 61**
W RF/ICP 285 6.3 (He) 30 (Ar) 100 (Ar) +
15 (H2)
40 80 4120** 40** 61**
Mo GSP 250 6 (Ar) 40 (Ar) 10 (H2) 60 33 3100 132 65
Mo GSP 120 6 (Ar) 40 (Ar) 10 (H2) 60 33 3100 132 65
Al2O3 WSP 120 N2 – – 433 160 – – 50
Cr2O3 WSP 90 N2 – – 530 160 – – 50
Notes: * standard liters per minute; ** volumetric median; GSP = gas stabilized plasma; WSP =
water stabilized plasma; T s is substrate temperature; q c is carrier gas flowrate; q p is primary
(plasma) gas flowrate; q s is secondary (sheath) gas flowrate; P is torch power; T p is mean particle
temperature; v p is mean particle velocity; d mean is mean particle diameter.
Table 2
Feedstock Spray
technology
W
W
W
Mo
Mo
Al2O3
Cr2O3
RF/ICP
RF/ICP
RF/ICP
GSP
GSP
WSP
WSP
T s ,
�C
560
430
285
120
250
120
90
E,
GPa
182
179
17
45
43
48
43
Deposit Properties
E bulk ,
GPa
411
411
411
329
329
345
350
E
E bulk
0.44
0.44
0.04
0.14
0.13
0.14
0.12
� h coating ,
mm
0.09
0.02
0.06
0.15
0.27
0.33
0.30
0.60
0.42
0.46
0.28
0.31
0.35
0.44
h splat ,
mm
6.30
6.30
7.00
4.60
4.50
7.00
7.50

Microstructure and Fracture Morphology ...
splats to disc-splats, [5]) of W on W system is situated in that range. No similar change
was detected for Mo, probably due to a low substrate temperature. The transition
temperature of Mo on steel is reported in the range of 300–400�C in [6] and around 300�C
in [7].
Fig. 1. The influence of substrate temperature on coating microstructure for W and Mo coatings.
Fig. 2. The elastic modulus and relative density of Mo and W deposits vs. the substrate temperature.
The metallographic samples of ceramic deposits prepared by ion milling showed an
extensive porosity network formed by intersplat pores and intrasplat cracks. In order to
visualize the crystal structure, the specimens were ruptured on a tensile machine and the
coating fracture was observed (Fig. 3). The micrographs show columnar grain structure of
the splats and dendritic structure of spherical particles (that impacted in solid state). The
transition temperature for ceramic materials is supposed to be lower than that for metals
(in the range between 100 and 200�C, [8]). Thus, it is possible that ceramic coatings were
deposited above the transition temperature, as suggested by the splat morphology.
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O. Kováøík and J. Siegl
Fig. 3. The fracture surfaces of ceramics deposits showing lamellar structure of the deposit and
spherical particles.
Conclusions. The coating structure of the deposits investigated consists of
individual splats and a porosity network formed by intersplat pores and intrasplat cracks.
More intrasplat cracks occurred in ceramic deposits due to its brittle nature. Dense W
deposits with a high modulus were obtained at an elevated substrate temperature.
Acknowledgment. This research has been supported by the Czech Science Foundation through
Grant No. 106/05/0483 “Influence of Microstructure on Mechanical Properties of Thermally
Sprayed Materials.”
1. O. Kováøík, S. Xue, X. Fan, and M. Boulos, “RF plasma deposition of refractory metals: Case
study for tungsten,” in: B. R. Marple, M. M. Hyland, Y. C. Lau, et al. (Eds.), Building on 100
Years of Success, Proc. of the 2006 International Thermal Spray Conference (Seattle, USA),
ASM International (2006), pp. 215–218.
2. J. Matejicek, S. Sampath, D. Gilmore, and R. Neiser, Acta Mater., 51, No. 3, 873–885 (2002).
3. J. Dubský, B. Kolman, and M. Vyšohlíd, in: E. Lugscheider and P. A. Kammer (Eds.), Proc.
of the United Thermal Spray Conference (UTSC 99), Verlag für Schweien und Verwande
Veflahren, D.V.S-Verlag (1999), pp. 659–663.
4. O. Kováøík, J. Nohava, J. Siegl, and P. Chraska, J. Therm. Spray Technol., 14, No. 2, 231–238
(2005).
5. P. Fauchais, M. Fukumoto, A. Vardelle, and M. Vardelle, J. Therm. Spray Technol., 13, No. 3,
337–360 (2004).
6. X. Jiang, J. Matejicek, and S. Sampath, Mat. Sci. Eng. A, 272, No. 1, 189–198 (1999).
7. X. Jiang and S. Sampath, Mat. Sci. Eng. A, 304-306, 144–150 (2001).
8. L. Bianchi, F. Blein, P. Lucchese, et al., in: C. Berndt and S. Sampath (Eds.), Thermal Spray
Industrial Applications, ASM International, Metals Park, Ohio (1994), p. 569.
Received 28. 06. 2007
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UDC 539.4
Near Surface Modification Affected by Hydrogen Interaction: Global
Supplemented by Local Approach
Y. Katz, 1,a N. Tymiak, 1 and W. W. Gerberich 1
1
Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis,
USA
a roy@roykatz.com
The current study is centered on elastic-plastic solid interaction with hydrogen. Here, the
environment is free hydrogen, from either external or internal origins providing as such aggressive
effects. In this context, near surface displacement occurred, beside microcracking onset or growth,
significant interfacial weakening, as critical forms of mechanical degradation. Metastable
austenitic stainless 316L steel was selected, in order to provide a comprehensive study on bulk
surfaces. Global findings on hydrogen effects were supplemented by nanoscale information. Only
for the nanosection, Ti/Cu thin films were also included, namely an additional small-volume case.
Samples have been charged with hydrogen under low fugacity conditions and the outcoming effects
have been sorted out by mechanical response tracking assisted by contact mechanics methodology.
Nanoindentation and continuous scratch tests were utilized supplemented by Scanning Probe
Microscopy (SPM) visualization. Local resolution provided remarkable input to the global findings,
in terms of dislocation nucleation aspects, near surface modification, plastic localization and
microfracture onset. In thin layers, the effective work of the adhesion was reduced indicating
significant degradation that could be expressed quantitatively. Global/local benefits of the stainless
steel system under study made it possible to apply multiscale models describing complex micromechanical
processes.
Keywords: metastable austenitic steel, hydrogen interaction, nanotests, continuous scratch
tests, crystal plasticity.
Introduction. Hydrogen/metal interactive effects have significant implications on
surface behavior including structural integrity aspects due to crack stability transition.
Regardless the specific enhancing damage origins, irreversible displacement, microcrack
initiation and growth beside delamination require special concern from nano-, meso- up to
macrostructural scale. The striking point in the current study is based on small-volume
experiments and is mainly focused on how hydrogen affects small-volume mechanical
behavior. An appropriate factor in analyzing the basic interaction of hydrogen was
attributed to variations in the length scale. In elastic-plastic solids with no hydrogen,
consistent trends of the length scale have been already established. On this background,
hydrogen interaction could be screened for length scales regarding toughness or hardness.
The small-volume activity was mainly conducted in a metastable stainless steel system
with some findings in hydrogen affecting Ti/Cu thin film. However, a very extensive
background was previously established as related to AISI 316L [1–3] regarding possible
events that are enhanced by hydrogen. Plastic displacement might have the end result of
fracture processes, namely embrittlement or load-bearing capacity limitations. Moreover,
surface modification caused by environment introduces issues regarding tribological
contact insights. Nanotests also promise new experimental options with implications on
quantification of early wear. These elements are highly accentuated in a metastable system
in which phase stability is dominated by mechanical or chemical aspects.
Experimental Procedures. Global Approach. Macrostudies in austenitic stainless
steel included AISI 304, 316 and 310 steels. Mechanical response was studied using
fracture mechanics methodology [1–3]. In metastable systems with no hydrogen, austenite
decomposition occurred below the Md temperature. However, presence of hydrogen
© Y. KATZ, N. TYMIAK, W. W. GERBERICH, 2008
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Y. Katz, N. Tymiak, and W. W. Gerberich
enhances martensitic transformation, resulting also in delayed microcracking and ductility
reduction [4–6]. Austenite products were identified using X-ray diffraction and the
Mossbauer spectroscopy analysis.
Local Approach. For 316L metastable stainless steel nanotests were conducted on
top of global tests. Thus, indentation tests to a prescribed load of 100 �N were performed
with Hysitron nanoindentation instrument using conical indenter with 400 nm tip radius
curvature. Tests were performed prior to hydrogen charging, instantly, post charging and
one day after charging. Beside nanoindentation, lateral continuous scratch tests were
performed. Hydrogen was also charged by 1MNaOH cathodic charging under current
densities in the range of 10 to 500 mA/cm 2 . Fine features’ visualization was carried out by
Scanning Electron Microscopy (SEM) and by Atomic Force Microscopy (AFM). In
addition, other experiments regarding thin films affected by hydrogen were conducted.
Here, thin films on SiO2 substrate with and without hydrogen were probed allowing some
classification of Cu and Cu/Ti/SiO2 interfacial bonds to be assessed.
Experimental Results. Macromethodology. It became evident that hydrogen
provided either by electrolytic cathodic charging or by high-temperature pressure gaseous
charging preserves fundamental findings of transformation and alternative fracture modes.
The transformation reaction was identified resulting in hexagonal close-packed and
body-centered-tetragonal martensitic products. Mechanical response degradation with
hydrogen became apparent in all parameters starting with significant surface relief.
Delayed microcracking, hydrogen affected near surface layer and modification, as well as
enhanced crack growth and degradation of the fatigue strength, were established.
Local Findings. Reproducible displacement excursions at an average load of 200 �N
were observed for the noncharged samples. This finding based on nanoindentation
load-displacement curves was attributed to plasticity initiation since unloading prior to the
excursion load yielded no residual deformation. In contrast, yield initiation in charged
specimens occurred at 100–650 �N. One day after charging the yield point ranged
between 300–350 �N (Fig. 1). With regard to the scratch test, hydrogen interaction
increased localized plasticity along given slip bands by as much as a factor of three. These
direct results become highly relevant in the near surface modification evolution in the
dynamic sense. In principle, quantitative local strain arguments could be based on
measurements of the surface slip height habits (h) and the spacing (s). Surface ultrafine
features along the scratch pile-up as well as perpendicular to the scratch pile-up indicated
dramatic effects of hydrogen on microplasticity. Even under low fugacity charging,
significant variations were measured providing eventually building blocks for multiscale
modeling efforts. The Cu/SiO2 thin film result is shown in Fig. 2 by emphasizing the
increase of delamination area affected by the hydrogen environment.
Fig. 1. Load at plasticity initiation vs. time after hydrogen charging.
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Near Surface Modification Affected by Hydrogen Interaction ...
a b
Fig. 2. Indentation induced delaminations in 500 nm Ti/Cu film on noncharged (a) and hydrogen
charged (b) samples.
Discussion. Surface modification due to environmental infraction in metastable
austenitic stainless steel has at least two origins: firstly, displacements caused by phase
stability associated with martensitic phases and, secondly, hydrogen-enhanced localized
plasticity that can be measured. These results are experimentally substantiated by the
combined program of global/local approach. Pseudo-phases were identified during the
transient time by consistent X-ray diffraction and the Mossbauer spectroscopy analysis,
and internal friction results were obtained [7]. Moreover, extensive activities by Birnbaum
[8] emphasized the local approach by sophisticated in situ Transmission Electron
Microscope (TEM) observations. In this context, the current findings by nanomechanical
methodology explore fundamental insights in terms of localized slip by AFM as enhanced
by hydrogen uptake. Beside measured local displacements, results like microcracking and
other damage factors introduce additional detrimental surface modification elements. The
described investigation with local resolution of dislocation dynamics bounded to crystal
plasticity reflects on wear or tribological contact. For example, Kubota et al. [9] addressed
the issue of fretting fatigue in austenitic stainless steel system by concluding the
significant life decrease that was caused by hydrogen interaction. Such results combined
with basic inherent mechanics become more understandable and can shade light on
structural integrity phenomena.
Conclusions. Viable hydrogen embrittlement models [1, 2] can be based on the
microapproach input, particularly in terms of dislocation shielding mechanisms developed
for the hydrogen-enhanced local decohesion model. The nanoscale results also emphasize
the inclusion of microplasticity variations that can explain the wide range data on
deformation/hydrogen interaction in elastic-plastic crystalline solids. The following
conclusions are made:
1. Hydrogen concentration near the surface in 316L metastable austenitic stainless
steel raised the dislocation nucleation load by more than a factor of two.
2. In copper thin film on silica substrate, hydrogen interaction decreases work of
adhesive.
3. Nanomechanical tests combined with probe microscopy provide critical
experiments resolving the scale relationship to be involved in the embrittlement phenomena.
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Y. Katz, N. Tymiak, and W. W. Gerberich
4. In metastable stainless steel with hydrogen, austenite decomposition enhances
surface relief, localized plasticity, microcracking or delimitation, which cause significant
surface modification with implication to tribological contact effects.
1. M. J. Lii, X. F. Chen, Y. Katz, and W. W. Gerberich, Acta Metal. Mater., 38, 2435 (1990).
2. X. Chen, T. Foecke, M. Lii, Y. et al., Eng. Fract. Mech., 35, 997 (1989).
3. H. Mathias, Y. Katz, and S. Nadiv, in: T. N. Vezirogla (Ed.), Metal–Hydrogen Systems,
Pergamon Press, Oxford (1982), p. 225.
4. H. Houng and W. W. Gerberich, Acta Metal. Mater., 42, 639 (1994).
5. D. G. Ulmer and C. J. Altsetter, Acta Metal. Mater., 39, 1237 (1991).
6. D. P. Abraham and C. J. Altsetter, Metal. Trans., 26A, 2859 (1995).
7. V. G. Gavrilijuk, H. Hanninen, A. V. Taraschenko, et al., Acta Metal. Mater., 43, 559 (1995).
8. H. K. Birenbaum, I. M. Robertson, P. Sofronis, and D. Teter, in: CDI 96, Institute of
Materials, UK (1997), p. 172.
9. K. Yanagbihara, S. Oayanagi, M. Kubota, et al., J. Soc. Mat. Sci. Japan, 54, 1237 (2005).
Received 28. 06. 2007
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UDC 539. 4
Thin Surface Layer of Plasma Treated Polyethylene
V. Kotál, 1,a P. Stopka, 2 P. Sajdl, 3 and V. Švorèík 1
1 Department of Solid State Engineering, Institute of Chemical Technology, Prague, Czech Republic
2
Institute of Inorganic Chemistry, Academy of Sciences of the Czech Republic, Øe�, Czech
Republic
3 Department of Power Engineering, Institute of Chemical Technology, Prague, Czech Republic
a vladimir.kotal@vscht.cz
This paper reports on the effect of argon plasma on the high density polyethylene surface. The aim
is to alter the surface in a manner and scale resulting in a stronger metal/polymer valence. The
specimens are exposed to the direct current discharge, the irradiation time and power being
variables. Electron paramagnetic resonance and X-ray photoelectron spectroscopy (EPR and XPS,
respectively) are employed to determine the plasma effect. The surface wettability is studied by
goniometry. The plasma treatment leads to radical generation and activation of such agents as
oxygen, thus the surface wettability is significantly increased. The evolution of the treated surface in
different media is studied. The influence of an increased oxygen concentration and the storage
medium on the concentration gradient within the surface monolayers is proved. The EPR data show
a gradual and very slow decrease in the number of radicals present on the treated surface after
2000 h. Also evidence is given for partial dissolution of the treated surface in water.
Keywords: argon plasma, high density polyethylene, goniometry, X-ray photoelectron
spectroscopy, electron paramagnetic resonance.
Introduction. Polymers have been applied successfully in many fields such as
adhesion, biomaterials, protective coatings, friction and wear, composites, microelectronic
devices, and thin-film technology. In general, special surface properties with regard to
chemical composition, hydrophilicity, roughness, crystallinity, conductivity, lubricity, and
cross-linking density are required for successful applications in various fields. However,
the “raw-pristine” polymer surface is inert and the modification techniques need to be
used [1].
Plasma treatment, which is known to modify chemical and physical states of the
surface without altering the bulk properties, has become an important tool used in industry
[2, 3]. Plasma effect is versatile and strongly depends on the experimental conditions
chosen. Take for example polyethylene, its plasma treatment leads to creation of new
chemical groups, branching and crosslinking of macromolecules [2], and to formation of
low molecular weight oxidized structures. Owing to ablation, the surface topography of
the polymer is affected too. These alterations are also well known to result in the
formation of reactive sites for the interaction with the metal atoms such as copper and
aluminum. The metal polymer adhesion has been of highest interest recently and every
attempt to elucidate their interaction is greatly appreciated.
The aim of this study is introduction of reactive sites to the high density polyethylene
(HDPE) surface by argon plasma treatment. Further, the evolution of wettability, radical
concentration, and chemical structure is thoroughly investigated. The surface wettability is
studied by goniometry. X-ray photoelectron spectroscopy (XPS) is carried out to observe
the surface chemical structure and electron paramagnetic resonance spectroscopy is
employed for determination of the radical number. The experiment and the abovementioned
methods yield a complex insight into the evolution of the HDPE plasma treated
surface.
©V.KOTÁL, P. STOPKA, P. SAJDL, V. ŠVORÈÍK, 2008
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V. Kotál, P. Stopka, P. Sajdl, and V. Švorèík
Experimental. Polymer and Plasma Parameters Specification. Oriented HDPE in
the form of 50 �m thick foils was used in the present experiment. The foils were supplied
by Granitol Ltd., Czech Republic. The samples were treated in a direct current discharge
generated using Balzers SCD 050 device. The further discussed plasma effect was
obtained under the following conditions (gas purity 99.997% and the flow rate 0.3 l/s,
pressure 10 Pa, electrode distance 50 mm and its area 48 cm 2 , chamber volume approx.
1000 cm 3 , plasma volume 240 cm 3 , and power 8.3 W). The treated polymer samples were
stored under laboratory conditions, exposed to ambient atmosphere.
Diagnostic Methods. The contact angle, characterizing the surface wettability, was
measured using distilled water at room temperature with a Kernco G-1 goniometer
(Japan). The “static” contact angle dependence on the time after treatment was obtained
[4].
An Omicron Nanotechnology ESCAProbeP spectrometer was used to observe the
treated surface. The dimensions of the area analyzed were 2�3mm. The X-ray source was
monochromated at 1486.7 eV. The spectra were measured stepwise with a step in binding
energy of 0.05 eV. In order to understand the cause forthe decrease in the oxygen content
within several surface monolayers, the spectra were collected at six angles between the
detector and the surface normal (ARXPS). The data were processed by the CasaXPS
program.
The concentration of free radicals was determined using an electron paramagnetic
resonance spectroscopy with an x-band spectrometer of type Elexsys E-540,
Bruker-Biospin with a relative error of 10%. The samples were placed in a quartz tube and
measured at room temperature. The experimental conditions were as follows: the
magnetic field range 600 mT, sweep time 180 s, magnetic modulation 0.4 mT, field
modulation 100 kHz. The standards Mn/ZnS and Cr/MgO were used for the g-factor
calibration and for quantitative evaluation of the spectra. Identification and determination
of signals were performed by comparison with the standards.
Results and Discussion. Goniometry. The dependence of the water contact angle on
the plasma treatment time is shown in Fig. 1. The time after the plasma treatment is a
parameter of the curves. The higher the treatment time the lower the contact angle,
namely: the angle decreases from 100� (pristine HDPE) to 10� (240 s treated HDPE). The
increasing time after the plasma treatment leads to an increase in the contact angle. The
increase is more distinct for longer plasma treatments. As has been reported in a recent
study [5], the present measurements confirm the dependence of the contact angle
(wettability) on the time after the Ar plasma treatment. The cause for this is the diffusion
of the low-mass oxidized fragments and orientation of the polar groups towards the
specimen bulk and this phenomenon is referred to as hydrophobic recovery [6, 7].
Electron Paramagnetic Resonance Spectroscopy (EPR). The number of radicals
formed on the surface was monitored by the EPR. Figure 2 shows the number of radicals
for samples stored in different “media.” The “water” sample was stored in water for 12
hours, and then dried and examined. The “air” sample was kept in an ambient atmosphere.
The lower number of radicals for a “water” sample results from the storage in water,
which caused the removal of low-molecular-weight oxidized material from the treated
surface [8]. This material contains a portion of the introduced radicals. Figure 2 also
clearly shows a slow decrease in the number of radicals during storage. The free radical
centers are “trapped” inside the crosslinked layer and are of low chemical reactivity, even
if the surface is exposed to water [9].
X-ray Photoelectron Spectroscopy. The chemical structure of the plasma treated
HDPE stored subsequently in air or water was examined using the XPS. It was reported
that the surface of the Ar plasma treated HDPE contains groups of pristine PE (–CH2) and
oxygen introduced during the treatment (–C=O, –COO, and –COC–) [5].
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Thin Surface Layer of Plasma Treated Polyethylene
Fig. 1 Fig. 2
Fig. 1. Evolution of the contact angle dependence on the plasma treatment time. The numbers
represent hours elapsed after the treatment.
Fig. 2. Dependence of spin number of the plasma treated samples on time after the treatment. The
samples were treated successively stored 12 h in water (�) resp. air (�) and measured.
Fig. 3. The dependence of oxygen concentration on the detector to surface normal angle. The
samples were plasma treated and preceding the measurement stored in air for 1 h (Air 1) and 24 h
(Air 24). The sample (Water 24) was stored 24 h in water.
In the EPR study it we found that a portion of the treated surface is dissolved during
storage in water. In order to confirm this result and also to learn more about the evolution
of the first surface layers (within approx. 5 nm) after the treatment, the angle-resolved
XPS has been carried out [10, 11]. Figure 3 shows the dependence of the oxygen
concentration on the angle between the surface normal and the detector. The higher the
angle, the thinner layer is studied, i.e., an angle of 80� allows studying the structure of the
surface monolayers. Figure 3 shows that the oxygen concentration in the samples treated
and stored in air for 1 h and 24 h (Air 1 and Air 24, respectively) decreases towards the
bulk of the sample. It has already been stated that the surface is oxygenated during the
treatment. The post treatment oxygen incorporation is rather uncertain and some authors
are in favor of it [12] while others are not [13]. What is worth noticing is that the oxygen
concentration of the “Air 24” sample is lower than that of “Air 1.” This has been shown
by goniometry, the results of which proved increasing hydrophobic character after the
treatment, i.e., during aging. Another important conclusion made from the ARXPS data is
that the oxygen concentration in the water stored sample “Water 24” at high angles is
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V. Kotál, P. Stopka, P. Sajdl, and V. Švorèík
lower than that in the “Air 1”sample. This suggests that a portion of the surface, especially
of the oxidized material, is dissolved in water. This has been confirmed by the EPR in this
work, as well as by the IR spectroscopy of the material dissolved in water [8]. Finally, the
only explanation for the increase in the concentration of oxygen with a decrease in the
angle for the “Water 24” sample is that the oxygen concentration increases into the depth
of the material(within the nm scale). At a depths of the order of 10 nm we expect a sharp
decrease in oxygen concentration. This is confirmed by Rutherford back scattering (RBS)
analyses carried out on this sample [8].
Conclusions. The effect of the HDPE treatment in the Ar plasma discharge on its
properties has been studied by different techniques. We have proved that the dischargeinduced
surface alterations lead to an immediate increase in the surface wettability.
Moreover, this effect is not permanent and the wettability decreases during the time after
treatment. The EPR data show a gradual and very slow decrease in the number of radicals
present on the treated surface; partial dissolving of the treated surface in water is also
observed. The backbone of this report is the XPS observations, which revealed an
increased oxygen concentration within the treated surface. Furthermore, it has been
proved that the water storage causes an increase in the oxygen concentration gradient
within the surface monolayers. On the contrary, when the sample is stored in air, the
oxygen gradient decreases.
Acknowledgments. This work was supported by the GA ASCR under the project
KAN400480701 and Ministry of Education of the CR under research program No. LC 06041.
1. C. M. Chan, T. M. Ko, and H. Hiraoka, Surf. Sci. Rep., 24, 3 (1996).
2. M. R. Wertheimer, A. C. Fozza, and A. Hollander, Nucl. Instrum. Meth. B, 151, 65 (1999).
3. P. K. Chu, J. Y. Chen, L. P. Wang, and N. Huang, Mater. Sci. Eng. R, 36, 143 (2002).
4. M. A. Grunlan, N. S. Lee, F. Mansfeld, et al., J. Polym. Sci., 44, 2551 (2006).
5. V. Švorèík, V. Kotál, P. Slepièka, et al., Nucl. Instrum. Meth. B, 244, 365 (2006).
6. F. Truica-Marasescu, P. Jedrzejowski, and M. R. Wertheimer, Plasma Process. Polym., 1, 153
(2004).
7. S. Guimond and M. R. Wertheimer, J. Appl. Polym. Sci., 94, 1291 (2004).
8. V. Švorèík, V. Kotál, P. Slepièka, et al., Polym. Deg. Stab. (submitted).
9. M. Kuzuya, T. Kawaguchi, M. Nakanishi, and T. Okuda, J. Chem. Soc. Faraday Trans., 82,
1441 (1986).
10. S. Oswald, R. Reiche, M. Zier, et al., Appl. Surf. Sci., 252, 3 (2005).
11. P. J. Cumpson, J. Elec. Spec. Rel. Phenomena, 73, 25 (1995).
12. M. Kuzuya, S. Kondo, M. Sugito, and T. Yamashiro, Macromolecules, 31, 3230 (1998).
13. O. Ochiello, Proc. of the 7th Int. Conf. on SIMS (1990), p. 789.
Received 28. 06. 2007
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UDC 539. 4
Theoretical and Experimental Investigation of the Dissipated and Stored
Energy Ratio in Iron under Quasi-Static and Cyclic Loading
O. Plekhov, 1,a S. Uvarov, 1,b and O. Naimark 1,c
1 Institute of Continuous Media Mechanics, RAS-Laboratory of Physical Foundations of Strength,
Russian Academy of Sciences, Perm, Russia
a poa@icmm.ru, b usv@icmm.ru, c naimark@icmm.ru
The problem of energy storing (cold work accumulation) in metals was intensively investigated both
theoretically and experimentally during all last century but a general theoretical conception of the
process was not created. This work is devoted to an experimental investigation of energy dissipation
in metals under plastic deformation and to the development of a thermodynamic model to study the
cold work accumulation under plastic deformation and failure. The proposed model is based on a
statistical description of collective properties of mesoscopic defects and on dividing the plastic
deformation into two parts (dissipative and structural). The structural plastic strain was considered
as an independent thermodynamic variable that allowed us to determine the thermodynamic potential
of the system. The derived constitutive relations were applied for numerical simulation of tensile
and cyclic tests. The numerical results demonstrate a good agreement with experimental data.
Keywords: cold work, energy dissipation, mesodefect evolution.
Introduction. The kinetics of the microstructure of metallic materials has been the
subject of much experimental investigations. The available data indicate that the
deformation of metals, especially plastic flow, is characterized by high dislocation activity
and specific mesodefect patterns. The evolution of these structures, accompanied by
failure and rotation of mesovolumes of the material, leads to generation of high internal
stresses and, as a consequence, to energy storage in a specimen. The problem of the
dependence of the storage energy Wst on the plastic work Wp �� ~
:(
~
�� ~
�e ) is widely
covered in literature [1–3] but their relation is still an open question. A generally accepted
assumption, W�02 . Wp, which is often justified by citing the early study of Taylor et al.
[4], is hardly applicable to many mechanical processes [3].
The basic theoretical problem of the models describing the energy balance under
plastic deformation is determination of new structure-sensitive parameters. The plastic
deformation, conventionally considered to be such a parameter, cannot be interpreted as
an independent thermodynamic variable.
Naimark et al. [5] developed an original method for describing the damage kinetics
using a statistical description of a mesodefect ensemble. Based on the statistical description
of the problem, it is possible to determine characteristic responses of solids with defects
and to work out an appropriate constitutive model. We use this approach to define
thermodynamic internal variables and to obtain nonlinear kinetic equations that describe
the energy balance in metals under plastic deformation. The plastic deformation is divided
into two parts (“pure” plastic deformation and “structural” or “potential” deformation),
and only one part (the structural deformation) is interpreted as an independent thermodynamic
variable. The obtained kinetic equations are used to describe the thermal
behavior of metals (for example, of pure iron) subjected to tensile and cyclic tests. We
present numerical simulation that incorporates our model and shows that theoretical
predictions and experimental results are in good quantitative agreement.
Thermodynamic Model. A general thermodynamic process obeys the momentum
balance equation and the first and second laws of thermodynamics. In the case of small
deformations, these equations involve the following thermodynamic quantities: strain and
© O. PLEKHOV, S. UVAROV, O. NAIMARK, 2008
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O. Plekhov, S. Uvarov, and O. Naimark
stress tensors ~ � and ~ �, heat supply r, and specific Helmholtz free energy F. Assuming
the following kinematic relation for the material under study ~ ~ ~ ~ ~ e p
�� � �� �p��( T�T �)
,
where ~ � e is the elastic strain tensor, ~ � p is the plastic strain tensor (related to the defect
motion), ~ p is the defect-induced strain tensor (structural part of the plastic deformation),
~
� is the tensor of the thermal expansion coefficient, and T� is the reference temperature,
we can write the following equation for the solid temperature evolution:
cT� e p
�Q�Q�r�� T ,
(1)
e
e
where Q � TF~
e :
T
~�
p p
� is heating due to the thermoelastic effect, Q �� ~
:
~� � �
�
( ~
): ~� : ~�
��F~ p p�TF~ p represents the inelastic contribution to the heating, c is the
pT
specific heat capacity, and Fx denotes the derivative of F with respect to x.
Analysis of the inelastic contribution to the heating gives the following relation for
the stored energy rate:
�TF ~
pT �F~
p
Wst
�
~ p
:(
~� �
~�
.
(2)
� � p)
To solve Eq. (2), one should determine the structural plastic deformation ~ p.
The structural parameters associated with typical mesoscopic defects (microcracks,
microshears) were introduced in [5] as the derivatives of the dislocation density tensor.
Those defects are described by symmetric tensors of the form ~ s�svv �� for microcracks
and ~
s s( vl lv )
T
�12 �
�� ��
for microshears. Here � v is the unit vector normal to the base of a
microcrack or the microshear slip plane, � l is the unit vector in the direction of shear, and
s is the microcrack volume or the shear intensity for microshear. The average of the
“microscopic” tensor ~ s gives the macroscopic tensor of the microcrack or the microshear
density ~ ~ p�n s , where n is the defect concentration.
Statistical description of the microcrack (microshear) ensemble was developed in
terms of the solution of the Fokker–Plank equation in the phase space of the possible
states of the microscopic variable ~ s linking the size s and the � �
v, l orientation modes.
The obtained solution allowed the definition of the part of the free energy caused by
defects F ~. p The “equilibrium” correlation of the defect density tensor and the applied
stress is given by the formula (for a one-dimensional case) �Fp ( �, p) �p�0.
The
solution to the latter relationship depends on a new structural-scaling parameter �. This
parameter indicates the scale distribution of the defect density tensor in a specific volume
and plays the role of the second structural variable related to the multiscale nature of
damage accumulation.
Finally, assuming linear relations between thermodynamic forces and fluxes, we can
obtain the following constitutive equations:
~� p
� �L pF~ e �L p ( F~ e �F~
),
� � � p � p
~� p�L p ( F~ e �F~ )
� � p �L p F e ,
� p �
�
�
� LF.
� �
One-Dimensional Tensile Loading. The experimentally investigated material was
annealed iron. During all tests, an infrared camera (CEDIP Jade III MWR) was used to
record the temperature field evolution on the specimen surface. The main technical
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(3)

Theoretical and Experimental Investigation ...
characteristics of the camera are as follows: spectral range 3–5 �m, maximum picture size
320�240 pixels, maximum framing rate 500 Hz, NETD < 25 mK at 300 K, and digital
conversion 14 bits. To increase the surface emissivity properties, the specimen surface
was painted black (mat paint) after polishing.
The experimentally obtained temperature field was numerically processed to
determine the space-time evolution of the heat sources and the stored energy value. The
typical results are presented in Fig 1.
a b
Fig. 1. Space–time evolution of the heat sources (in W/m 3 ) in the longitudinal specimen section (a),
stress–strain, mean temperature variation, and stored energy rate curves (b) obtained during the test.
(The stress and temperature difference were normalized by the corresponding maximum values.
Maximum stress is 27 MPa, maximum temperature difference is 4�C.)
To simulate the elastic-plastic transition accompanied by the heat wave propagation,
the system of equations (1) and (3) together with the momentum balance equation was
numerically solved. Figure 2 presents the experimentally and numerically determined
space-time evolution of the heat sources in iron under elastic-plastic transition.
a b
Fig. 2. Experimentally (a) and numerically (b) obtained space-time evolution of the heat sources in
the longitudinal specimen section under elastic-plastic transition.
Cyclic Loading. The developed model allows us to simulate temperature evolution
under cyclic loading. The main feature of cyclic loading is the creation of many different
dislocation structures during the test. In terms of the model, it means that both structuresensitive
parameters ~ p (deformation caused by defect initiation) and � (describing the
arrangement of dislocation ensemble) vary and interact during the test. Figure 3 presents
the temperature evolution in iron during the numerical test. We obtain three (experimentally
observed) stages of temperature evolution during the fatigue test: (I) initial temperature
increase, (II) constant temperature region, (III) abrupt temperature increase before failure.
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O. Plekhov, S. Uvarov, and O. Naimark
Fig. 3. Temperature evolution under cyclic loading during a numerical test.
Conclusions. Experimental and theoretical investigations of the energy storage and
dissipation in metals allow us to propose a thermodynamic model to describe the energy
balance under plastic deformation of metals. The key point of the model is the presentation
of plastic deformation in terms of two variables: plastic strain tensor (related to the
dissipation effect) ~ � p and defect-induced strain tensor (related to the stored energy) ~ p.
This makes it possible to consider the structure-related part of plastic deformation as a
thermodynamic variable and to formulate a corresponding nonequilibrium thermodynamic
potential (free energy). The developed approach has been successfully applied to the
simulation of nonlinear thermal effects observed under quasi-static and cyclic loading of
iron.
Acknowledgments. The authors thank the laboratory LAMEFIP ENSAM (personally Dr. T. Palen-
Luc and Dr. N. Saintier) for the help in the experimental investigations. The work was partly
supported by the grants of RFBR (05-08-33652, 07-08-96001, 07-05-96019).
1. M. B. Bever, D. L. Hilt, and A. L. Titchener, Prog. Mater. Sci., 17, 1 (1973).
2. R. Kapoor and S. Nemat-Nasser, Mech. Mater., 27, 1 (1998).
3. P. Rosakis, A. J. Rosakis, G. Ravichandran, and J. Hodowany, J. Mech. Phys. Solids, 48, 581
(2000).
4. W. S. Farren and G. I. Taylor, Proc. Roy. Soc. London, A107, 422 (1925).
5. O. Naimark, M. Davydova, O. Plekhov, and S. Uvarov, Phys. Mesomech., 2, 43 (1999).
Received 28. 06. 2007
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UDC 539. 4
Collective Modes in the Microshear Ensemble as a Mechanism of the Failure
Wave
O. Naimark, 1 O. Plekhov, 1 W. Proud, 2 and S. Uvarov 1,a
1 Institute of Continuous Media Mechanics, Russian Academy of Sciences, Perm, Russia
2 Cambridge University, Department of Physics, Cavendish Laboratory, Cambridge, UK
a usv@icmm.ru
Results of theoretical and experimental study of failure wave phenomena are presented. A
description of the failure wave phenomenon was proposed in terms of a self-similar solution for the
microshear density. The mechanisms of failure wave generation and propagation were classified as
a delayed failure with the delay time corresponding to the time of excitation of self-similar blow-up
collective modes in a microshear ensemble. Experimental study of the mechanism of the failure
wave generation and propagation was carried out using a fused quartz rod and included the Taylor
test with high-speed framing. The results obtained confirmed the “delayed” mechanism of the
failure wave generation and propagation.
Keywords: mesodefect evolution, failure waves.
Introduction. The phenomenon of a failure wave in brittle materials has been the
subject of intensive study during the last two decades [1–3]. The term “failure wave” was
introduced by Galin and Cherepanov [4] as the limit case of damage evolution, where the
number of microshears is large enough for the determination of the front with a
characteristic group velocity. This front separates the structured material from the failed
area. Rasorenov et al. [1] were the first to observe the phenomenon of delayed failure
behind an elastic wave in glass. Such a wave was introduced by Brar and Bless in [5],
where the concept of a fracture wave was discussed to explain the nature of the elastic
limit. A failure wave appeared in shocked brittle materials (glasses, ceramics) as a
particular failure mode in which they lose strength behind the propagating front. Generally,
the interest to the failure wave phenomenon is initiated by the still open problem of
physical interpretation of traditionally used material characteristics such as the Hugoniot
elastic limits, dynamic strength, and relaxation mechanism of elastic precursor.
Qualitative changes in silicate glasses behind the failure wave, e.g., an increase in
the refractive index, allowed Gibbons and Ahrens (1971) to qualify this effect as the
structural phase transformation. These results stimulated Clifton [6] to propose a
phenomenological model in which the failure front was assumed to be a propagating
phase boundary. According to this model, the mechanism of failure wave nucleation and
propagation results from the local densification followed by shear failure around the
inhomogeneities triggered by the shock.
Using high-speed photography, Paliwal et al. [7] obtained real-time data on the
damage kinetics during dynamic compressive failure of a transparent AlON. The results
suggest that final failure of the AlON under dynamic loading was due to the formation of
a damage zone with unstable propagation of the critical crack.
Statistical Model. The description of the failure wave phenomenon was proposed
by Naimark et al. [8, 9] after analyzing the damage localization dynamics in terms of a
self-similar solution for the microshear density. This solution describes qualitative changes
in the microshear density kinetics that allows defining failure waves as a specific (“slow
dynamics”) collective mode in the microshear ensemble that could be excited due to the
pass of a shock wave. Structural parameters associated with typical mesodefects were
introduced as a macroscopic tensor of the defect density , which coincides with the
© O. NAIMARK, O. PLEKHOV, W. PROUD, S. UVAROV, 2008
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O. Naimark, O. Plekhov, W. Proud, and S. Uvarov
deformation induced by defects. Taking into account the large number of mesoscopic
defects and the influence of thermal and structural fluctuations involved in the damage
accumulation process, the formulation of a statistical problem concerning the defect
distribution function was proposed by Naimark [9] in terms of the solution to the
Fokker-Plank equation in the phase space of characteristic mesodefect variables.
The statistical description allowed us to propose a model of a solid with defects
based on the appropriate free energy form. A simple phenomenological form of the part of
free energy caused by defects (for the uniaxial case ) is given by a sixth order expansion,
which is similar to the Ginzburg–Landau expansion in the phase transition theory [9]:
1
2 1 4 1
6 2
F� A( 1���*
) p � Bp � C( 1���c
) p �D�p�� ( �l
p)
. (1)
2
4 6
Here the gradient term describes non-local interaction in the defect ensemble; A, B, C,
and D are positive phenomenological material parameters, and � is the nonlocality
coefficient. The damage kinetics is determined by the evolution inequality
�F �t�( �F �p)� p�( �F ��) ��
�
0 ,
(2)
that leads to kinetic equations for the defect density p and scaling parameter �:
p� ��� ( �F �p�� �x ( ��p � x )),
(3)
p l l
�
�
��� �F ��,
(4)
�
where � p and �� are kinetic coefficients. Analysis of Eqs. (3) and (4) shows that the
scaling parameter � determines the reaction of a solid to the defect growth. If ���c , the
evolution of the defect ensemble is governed by spatial-temporal structures (S 3 )ofa
qualitatively new type characterized by an explosive (“blow-up”) accumulation of defects
as t ��c in the spectrum of spatial scales. The “blow-up” self-similar solution is the
precursor of the crack nucleation due to a specific kinetics of damage localization,
p�g( t) f( �), ��x L , g( t) �G( 1 �t
� ) ,
(5)
c c
where � c is the so-called “peak time” ( p �� at t �� c),
Lc is the scale of localization,
and G� 0 and m� 0 are the parameters of non-linearity, which characterise the free
energy release rate for ���c . The function determines the defect density distribution in
the damage localization area. Equation (3) describes the characteristic stages of damage
evolution. As the stress at the shock wave front approaches the critical value � c , the
properties of the kinetic equation (3) change qualitatively (for p� pc) and the damage
kinetics is subject to the self-similar solution [Eq. (5)]. The method for the solution of this
problem was developed by Kurdjumov [10]. It allowed the estimation of � f and the
definition of the failure front propagation kinetics:
�m
12 / ��[ 2( ��1)] ( ����1) [ 2( ��1)]
x � � � S t
. (6)
f f
0
Equation (6) determines self-similar regimes of the failure wave propagation, which
depends on the values of the parameters � and �. For instance, for the values of the
parameters ����1, a failure wave will be generated as the subsequent excitation of a
“blow-up” damage localization area arising after the shock wave pass with the delay time
t c .
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Collective Modes in the Microshear Ensemble ...
Numerical simulation of the damage kinetics [11] based on Eq. (6) for the conditions
of the plate impact test confirmed the mechanism of the failure wave generation predicted
by the aforementioned self-similar solution (Fig. 1).
Fig. 1. Simulation of the shock (S) and failure (F) wave propagation for the condition of the plate
impact test. The photos correspond to different times of the shock and failure wave propagation.
Experiment. An experimental study of the failure wave generation and propagation
was realized for the symmetric Taylor test performed on 25 mm-diameter fused-quartz
rods [11]. Figure 2 shows processing of photos obtained by a high-speed photography for
an experiment with a flyer rod traveling at 534 m/s at impact. The flyer rod was traveling
from the left to the right. In the first frame (0.3 �s after impact), two vertical dark lines are
observed. The line on the left is the impact surface. The line to the right is a shock wave
that can be clearly seen propagating at a higher velocity in front of other waves in the
subsequent frames.
Fig. 2. Processing of high-speed photos of the shock and failure wave propagation. Three dark
zones correspond to the images of the impact surface (�), failure wave (�), and shock wave (�).
Based on the measurements from the photographs, the first front was calculated to
slow down from the velocity approximately equal to the longitudinal wave speed in fused
quartz (5.96 km/s) during the initial 2.1 �s after impact to 52 . �03 . mm/�s after 3.9 �s.
Another front is observed in the frames labeled 1.5 and 1.8 �s after impact. By the 2.1 �s
after impact, it became the failure front (marked by a square). The 1D strain state will
exist until the release waves from the outer edges converge along the center of the
specimen. Therefore, the development of failure is under the same conditions as those
experienced during the plate impact, including the transition to the 1D stress state.
The second front appears at the 1.2 �s (0.6 �s after the first (elastic) front passes this
point). It is interesting to note that the second front appearing at the 1.2 �s does not
advance significantly until the material behind it becomes fully comminuted (opaque).
During this time the front velocity is V fw � 157 . km/s, which is close to that traditionally
measured in the plate impact test. However, the following scenario reveals an increase in
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O. Naimark, O. Plekhov, W. Proud, and S. Uvarov
the failure front velocity up to V fw � 4 km/s. The fact that the failure wave front velocity
approaches the shock front velocity supports the theoretical result concerning the failure
wave nature as “delayed failure” with the limit of the “delay time” corresponding to the
“peak time” in the self-similar solution (5). The loss of transparency is caused by the
defect nucleation and occurs during the “blow-up” time after the induction time � l (the
time of the formation of the self-similar profile of defect distribution). Failure occurs after
the delay � d , which is the sum of the induction time � l , and the “peak time” � c (the
time of the “blow-up” damage kinetics). The steady-state regime of the failure wave front
propagation can be associated with the successive activation of the “blow-up” dissipative
structures under the condition where �d � �c.
The research was supported by the RFBR projects (Nos. 07-08-96001 and 05-01-
00863).
1. S. V. Rasorenov, G. I. Kanel, V. E. Fortov, and M. M. Abasenov, High Press. Res., 6,
225–232 (1991).
2. N. K. Bourne, Z. Rosenberg, J. Field, and I. G. Crouch, J. Physique IV, C8, 635 (1994).
3. G. I. Kanel, A. A. Bogach, S. V. Rasorenov, and Zhen Chen., J. Appl. Phys., 92, 5045–5052
(2002).
4. L. A. Galin and G. P. Cherepanov, Sov. Phys. Doklady, 167, 543–546 (1966).
5. N. K. Brar and S. J. Bless, High Press. Res., 10, 773 (1992).
6. R. J. Clifton, Appl. Mech. Rev., 46, 540–546 (1993).
7. B. Paliwal, K. T. Ramesh, and J. W. McCauley, J. Amer. Ceram. Soc., 89, 2128 (2006).
8. O. B. Naimark and V. V. Belayev, Phys. Combust. Explos., 25, 115 (1989).
9. O. B. Naimark, V. A. Barannikov, M. M. Davydova, et al., “Crack propagation: Dynamic
stochasticity and scaling,” Tech. Phys. Lett., 26, No. 3, 254–258 (2000).
10. S. P. Kurdjumov, in: Dissipative Structures and Chaos in Non-Linear Space, Utopia,
Singapure (1988), Vol. 1, P. 431.
11. O. B. Naimark, S. V. Uvarov, D. D. Radford, et al., in: Proc. Fifth Int. Symp. on Behavior of
Dense Media under High Dynamic Pressures, Saint Malo, France (2003), Vol. 2, pp. 65–74.
Received 28. 06. 2007
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UDC 539. 4
Relation between Mechanical Properties and Microstructure of Cast
Aluminum Alloy AlSi9Cu3
M. Panušková, 1,a E. Tillová, 1,b and M. Chalupová 1,c
1
University of Zilina, Faculty of Mechanical Engineering, Department of Materials Engineering,
Zilina, Slovak Republic
a marta.panuskova@fstroj.uniza.sk, b eva.tillova@fstroj.uniza.sk,
c maria.chalupova@fstroj.uniza.sk
One common material for engine applications is the AlSi9Cu3 alloy. This alloy has a good
castability, excellent machinability, medium strength, and low specific weight. The study was
focused on the investigation of the effect of the solution heat treatment on the microstructure and
mechanical properties of the alloy (strength – R m , hardness – HBS). The temperatures of the
solution heat treatment were 505�C, 515�C, and 525�C�5�C and the solution time ranged from 0 to
32 h (0, 2, 4, 8, 16, and 32 h). Alloy AlSi9Cu3 contained �-matrix, eutectic silicon, and other Feand
Cu-rich phases with different morphology (needle-like, Chinese script, skeleton-like, blocky,
etc.). The results obtained revealed the relation between the mechanical properties and the
morphologies of the eutectic silicon and the predominant copper-rich phase Al–Al2Cu–Si during the
solution treatment.
Keywords: aluminum cast alloys, microstructure, mechanical properties, intermetallic
phases, fracture zones.
Introduction. In industry, particularly in aerospace and automobile branches, there
is a tendency to reduce costs, prices, and weight of complete products. In this respect, of
importance are easy availability and the industry requirements for environmental
protection, i.e., recyclability of industry materials. Significant is the fact that the density of
steel materials is three times higher than that of aluminum alloys. The substitution of
aluminum alloys for magnesium ones is a momentous aim in the development of many
branches of industry, but magnesium alloys have a lot of disadvantages: the contact with
magnesium melts is hazardous that excludes their recycling possibilities [1].
Cost effectiveness of the production and application of aluminum alloys is being
constantly improved, e.g., at present an average European automobile contains about 90%
of recycled aluminum alloys out of the total share of aluminum alloys in an automobile
[1]. Al–Si cast alloys are extensively used in the automotive and aerospace industries due
to their excellent castability, good mechanical properties and wear resistance. The addition
of alloying elements such as Mg and Cu make these alloys heat treatable further
improving their mechanical properties and allowing their use in new, more demanding
applications (e.g., engines, cylinder heads, etc.). The most used heat treatment for these
Al–Si–Cu cast alloys is the solution treatment followed by age hardening that is required
for the precipitation of the Al2Cu hardening constituent. The solution heat treatment of
Al–Si–Cu cast alloys affects the microstructure of the alloy in three aspects, namely: the
dissolution of coarse Al2Cu, homogenization of the microstructure, improvement of
eutectic silicon morphology (fragmentation, spheroidization, and coarsening), and the
ensuing changes in the fracture zones [2].
The present study is a part of a larger research project, which was conducted to
investigate and to provide a better understanding of the influence of heat treatment on the
structure (structural analyses) and mechanical properties of cast Al–Si–Cu alloys. The
study was conducted on the most popular AlSi9Cu3 alloy that contains about 9% Si and
3% Cu.
© M. PANUŠKOVÁ, E. TILLOVÁ, M. CHALUPOVÁ, 2008
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M. Panušková, E. Tillová, and M. Chalupová
Table 1
Chemical Composition of AlSi9Cu3 Alloy
Element Si Cu Mn Zn Mg Ni Pb Fe Ti Al
wt.% 10.7 2.4 0.22 1.1 0.27 0.08 0.11 0.9 0.03 base
Experimental. Experiments were performed on AlSi9Cu3 cast alloy whose chemical
composition is given in Table 1. This alloy has a lower corrosion resistance and is suitable
for high-temperature (up to max. 250�C) applications (dynamically exposed casts). In this
case, the requirements to its mechanical properties are not so restrictive. This cast alloy
was produced at the Foundry Co. CONFAL, a.s., Slovenská Lupca.
Alloys of the Al–Si–Cu type are usually heat treated in order to develop higher
mechanical properties. Heat treatment involves solution and aging heat treatments during
which a series of changes in microstructure occur which then lead to the improvement of
strength. These changes in microstructure include the dissolution of precipitates,
homogenization of the cast structure, such as minimization of alloying element
segregation, spheroidization and coarsening of eutectic silicon, and precipitation of finer
hardening phases [3, 4]. Different solution heat treatment procedures were used to
evaluate their influence on the mechanical properties (tensile strength, R m , and hardness,
HBS) and on the morphology of the eutectic Si and Cu-rich phase (ternary eutectic
Al–Al2Cu–Si phase) and on ensuing changes in the fracture pattern.
The experiments were carried out in an electric induction furnace. The castings were
subjected to the solution treatment at three temperatures (505, 515, and 525�C) during the
periods of time ranging from 2 to 32 hours (0, 2, 4, 8, 16, and 32 h), then quenched in
warm water in the temperature range from 40 to 60�C, and aged naturally at room
temperature for 24 hours. The samples for microscopic analysis were prepared by
standard metallographic procedures (wet ground, DP polished with diamond pastes and
etched by Dix-Keller, HNO3 or MA [2]).
a b c
Fig. 1. Typical microstructure patterns in AlSi9Cu3 cast alloy (etched by a Dix Keller solution):
(a) �-matrix, platelets of eutectic Si; (b) Al5FeSi, Al–Al2Cu–Si phase; (c) Al15(MnFe)3Si phase –
“Chinese script.”
Generally, the as-cast microstructure of AlSi9Cu3 alloy comprises �-matrix, the
platelets of eutectic silicon (dark grey) (Fig. 1a) and many intermetallic phases. In this
alloy there were also observed the following intermetallic phases: the iron phase Al5FeSi
in the shape of black needles (Fig. 1b), which has a monoclinic crystal structure and
precipitates in interdendritic and intergranular regions as platelets [5]. Long Al5FeSi
platelets (more than 500 �m) can adversely affect the mechanical properties, especially
ductility, and they also lead to the formation of excessive shrinkage porosity defects in
castings. The Al5FeSi phase appears as a nucleation locality for Cu-rich phase Al–
Al2Cu–Si (Fig. 1b).
Another common iron intermetallic is the Al15(MnFe)3Si phase with a cubic crystal
structure [6]. This phase has a compact morphology in the form of “Chinese script”
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Relation between Mechanical Properties and Microstructure ...
(Fig. 1c) and thus it contains less initiated cracks as compared to the needle-like phase
Al5FeSi. The effect of the applied heat treatment on these iron-rich phases (Al5FeSi – 16%
Fe, Al15(MnFe)3Si – 14% Fe) is not significant and results only in partial segmentation of
these phases. Half or more of copper is found as a component of intermetallic compounds,
primarily, the Al2Cu phase with tetragonal crystal structure precipitates in two distinct
morphologies: Al2Cu and in the form of blocky phase with a high copper concentration
~38–40% Cu (ternary eutectic Al–Al2Cu–Si – Fig. 2a). These compounds that form at the
later stages of freezing are located in the interdendritic regions and at the grain
boundaries. Gradual dissolving of the Cu-rich phase occurs with increasing heat treatment
temperature (Fig. 2) and this fact is also confirmed by harness measurement results.
a b c
Fig. 2. The influence of heat treatment on the morphology of the Al–Al2Cu–Si phase: (a) untreated;
(b) at 515�C/4 hours; (c) at 525�C/4 hours.
The improvement of the eutectic silicon morphology and its distribution have the
most significant influence on the changes in the mechanical properties (Fig. 3). The
morphology of the eutectic silicon not subjected to heat treatment has the shape of
platelets (Fig. 3a). Figure 3b–d demonstrates changes in the eutectic Si morphology
caused by the solution treatment with a holding time of 8 hours. At temperatures of 505
and 515�C gradual spheroidization of the eutectic Si particles begins (Fig. 3b and c). As
the solution treatment continued to the temperature 525�C, the spheroidized particles
gradually grew larger (overcoarsed) (Fig. 3d).
a b c d
Fig. 3. Changes in the eutectic silicon morphology during heat treatment: (a) untreated; (b) heat
treated at 505�C during 8 hours; (c) heat treated at 515�C during 8 hours; (d) heat treated at 525�C
during 8 hours.
These changes in the eutectic Si influence the the characterpattern of the fracture
zones as well. In the eutectic silicon not subjected to the solution treatment, brittle fracture
fragile breach of the eutectic platelets and ductile failure of the �-matrix are observed.
With gradual spheroidization of the eutectic Si, the share of the ductile failure in the alloy
increases.
The microstructure of AlSi9Cu3 alloy is a reflection of the mechanical properties
(Fig. 4). The increase in the strength and hardness values is significant chiefly for
temperatures of 505 and 515�C and for holding time of 8 hours at the most. By the eighth
hour of the holding time the values of the mechanical properties (chiefly HBS) begin to
decrease. This trend is typical for all solution heat treatment temperatures and relates to
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M. Panušková, E. Tillová, and M. Chalupová
gradual coarsening of the eutetectic Si for the hold time longer than 8 hours (Fig. 4). At
the a temperature of 525�C a decrease in the values of the mechanical properties is
observed due to a significant coarsening of the eutectic Si (Fig. 3d).
Fig. 4. Changes in the mechanical properties of AlSi9Cu3 alloy during heat treatment.
With a deincrease in the heat treatment temperatures, gradual dissolution of the
Cu-rich phase takes place and this fact also confirms the results obtained for hardness and
tensile strength. With an increase in the solution treatment temperature, the hardness and
strength values increase to a maximum value at 515�C and then decrease. Hardness
correlates withis a reflection of the solution strengthening and silicon particle distribution
in the matrix. Temperature 515�C is a suitable appropriate temperature for this alloy.
Below this temperature, the solutionization process is insufficient, whereas above it,
overcoarsening of the Si particles and melting of Al2Cu melting Al2Cu occurs. These two
unsatisfied conditionsaspects all result in the reduction of hardness and strength.
Conclusions. The contribution investigation was focused on the influence of the
solution heat solution treatment on the microstructure and mechanical properties (R m and
HBS) of aluminum cast alloy AlSi9Cu3 for automotive applications. As shown by a the
results shown, the optimaoptimuml conditions of the heat solution heat treatment for this
alloy is are the temperature 515�C and holding time max. 8 hours. The changes of in the
microstructure confirmed that these outcomes. A heat treatment by temperature of heat
treatment 525�C get leads to gradual coarsening of the eutectic Si, decreasing ofing of the
values of the mechanical properties, values and dissolving dissolution of the ternary
eutectic Al–Al2Cu–Si.
Acknowledgments. The authors acknowledge the VEGA No. 1/2090/05 and No. 1/3153/06
for the financial support of this work.
1. J. Högerl, “Beeinflussung der Gefügemorphologie und der mechanischen Eigenschaften von
AlSi7Mg-Legierungen,” in: Fortschritt-Berichte VDI, Reihe 5, No. 457, VDI Verlag,
Düsseldorf (1996).
2. C. Kammer, Aluminium-Taschenbuch, Band 1: Grundlagen und Werkstoffe, Auflage 15,
Aluminium Verlag, Düsseldorf, (1995).
3. M. Kiš and P. Skoèovský, “Structure analysis of Sr modified AlSi10MgMn alloy,” in: Metody
Oceny Struktury Oraz Wlasnosci Materialow i Wyrobów, Ustron-Jaszowiec, Wyd. Pol.
Opolskiej, Poland (2005), pp. 89–94.
4. E. Tillová, M. Panušková, and M. Chalupová, “Influence of the solution treatment on the
structure and properties of cast AlSi9Cu3 alloys,” in: Fraktography’06, Stará Lesná (2006),
pp. 493–496.
5. E. Tillová, M. Panušková, and M. Chalupová, “Metallograpische Analyse von Al–Si–Cu
Gusslegierungen,” Berichte und Informationen, 2/2006, 14, Dresden, SRN (2006), pp. 49–55.
6. C. T. Rios and R. Caram, “Intermetallic compounds in the Al–Si–Cu system,” Acta
Mikroskopica, 12, No. 1, 77–81 (2003).
Received 28. 06. 2007
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UDC 539.4
Mechanisms of Fracture in Neutron-Irradiated 15Ch2MFA Steel
Š. Válek, 1,a P. Haušild, 1,b and M. Kytka 2,c
1 Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering,
Department of Materials, Prague, Czech Republic
2 Øe� Nuclear Research Institute, Øe�, Czech Republic
a Stepan.Valek@fjfi.cvut.cz, b Petr.Hausild@fjfi.cvut.cz, c kyt@ujv.cz
The influence of irradiation on fracture properties of 15Ch2MFA pressure vessel steel is studied.
The distribution of inclusions and carbides is characterized. The quantitative fractography of
broken Charpy specimens is carried out. The correlation of crack initiation energy and the area of
ductile fracture adjacent to the notch is identified. It is shown that most of the absorbed energy
belongs to the stage preceding the cleavage crack initiation. From the fracture surface of Charpy
specimens the distribution of ductile dimples is investigated. The relationship between the
distributions of ductile dimples and second phase particles is discussed.
Keywords: quantitative fractography, instrumented Charpy test, fracture energy,
ductile-to-brittle transition temperature.
Introduction. Neutron irradiation has the key influence on the ductile-to-brittle
transition temperature (DBTT) shift in 15Ch2MFA pressure vessel steel. In the DBTT
range, the prediction of fracture is complicated, since two fracture micromechanisms are
in competition. The final (brittle) fracture is frequently preceded by stable ductile tearing.
The ductile crack growth preceding the unstable fracture changes the stress-strain field
ahead of the crack tip (stress, strain, and constraint). We study the relation between the
unstable crack initiation and ductile crack extension in irradiated steel by means of
quantitative fractographic analysis.
Experimental Results. Tempered bainitic steel 15Ch2MFA used for manufacturing
of pressure vessel of VVER440 reactor was studied [1, 2]. The forged plate of 190 mm
thickness was subjected to the thermal treatment of normalizing at 1010�C/12h followed
by cooling in air, and tempering at 730�C/14h followed by furnace cooling. The chemical
composition is given in Table 1. The microstructure is the same for all three directions of
forging and the mean bainitic packet size is around 30 �m.
Table 1
Chemical Composition of 15Ch2MFA Steel (wt.%)
C Mn Si P S Cu Cr Ni Mo Co V As
0.18 0.50 0.31 0.014 0.016 0.10 2.80 0.07 0.65 0.009 0.009 0.009
Using Scanning Electron Microscope (SEM) Jeol JSM 5510 LV, the microanalysis of
second phase particles (inclusions) was carried out. X-ray analysis revealed the MnS
inclusions. The distribution of these inclusions was obtained using image analysis.
The image analysis was performed for different magnifications using images
obtained from both electron and optical microscopy. For the electron microscopy, the
backscattered electron signal (mode COMPO) was used. The total number of particles
found was 1882 and the investigated area was 28.8 mm 2 . Good agreement was found in
distribution of sizes of particles for both electron and optical microscopy and for different
magnifications.
© Š. VÁLEK, P. HAUŠILD, M. KYTKA, 2008
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Š. Válek, P. Haušild, and M. Kytka
Using SEM in the secondary electron mode, polished and etched specimens were
investigated in order to characterize the distribution of fine carbides in bainitic
microstructure. For the image analysis the magnification �10,000 was used. Within the
area of 1228 �m 2 there were found 1342 particles. It can be concluded that there are two
different populations of particles: MnS inclusions and carbides, each with its own
independent distribution of particle sizes.
The standard Charpy V-notch (CVN) specimens were taken at a depth position at
one quarter of the plate thickness from the surface (1/4t position) in the T (long
transverse) and T–S (long transverse-short transverse) orientations. The specimens were
enclosed and neutron-irradiated in the same capsules as standard surveillance specimens.
The chains contained the set of activation monitors (including fast as well as thermal
neutrons) and also fission monitors. Each capsule contained two rings of copper wire to
evaluate the azimuthal fluence. The capsules were irradiated in emptied surveillance
channels in the VVER 440-type nuclear reactor. The mean irradiation temperature was
estimated after evaluation of the melting temperature monitors to 275�C.
Transition curves of toughness of non-irradiated and neutron irradiated specimens
are illustrated in Fig. 1. The DBTT shift after �� � � �
23 2
97 . 10 n m is about 50�C. The
instrumented Charpy impact test allowed us to obtain the values of energy, forces, and
striker displacement associated with different stages of fracture (Fig. 2). After irradiation,
the force at general yield (Fgy ) increased, but striker displacement at unstable crack
initiation and force at crack arrest (FA ) decreased. The dependence of FA on temperature
and irradiation (Fig. 3) also indicates the DBTT shift.
Fig. 1 Fig. 2
Fig. 1. Transition curves of neutron irradiated and non-irradiated Charpy impact toughness KCV.
Fig. 2. Filtered record of signal from instrumented Charpy impact test of neutron irradiated and
non-irradiated specimens at room temperature.
The fractographic analysis of Charpy specimens broken in the region of ductile to
brittle transition revealed both cleavage facets and ductile dimples on the fracture
surfaces. Several types of cleavage initiation were observed. In non-irradiated specimens,
cleavage was triggered at lower temperatures on cracked or debonded second phase
particles (composed mainly of MnS) or initiated directly from the notch root. With
increasing temperature, the cleavage crack initiation was preceded by ductile crack growth
which forms a dimpled zone situated near the notch. As a consequence, cleavage initiated
in the vicinity of the ductile crack tip.
With increasing temperature, small amount of intergranular decohesion occurred and
cleavage was in some cases triggered by so produced flaw.
In neutron-irradiated specimens, the amount of intergranular decohesion
significantly increased at all temperatures (Fig. 4). As a consequence, at higher
temperatures cleavage frequently initiated in areas where the intergranular decohesion
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Mechanisms of Fracture in Neutron-Irradiated 15Ch2MFA Steel
Fig. 3 Fig. 4
Fig. 3. Dependence of FA on temperature and neutron irradiation.
Fig. 4. Intergranular decohesion on the fracture surface of neutron-irradiated Charpy specimen
broken at T �25�C. occurred. At low temperatures, cleavage initiated directly from the notch root, probably
due to the neutron induced hardening which significantly increased the stresses ahead of
the notch root.
In some cases, the cleavage crack arrest and re-initiation (pop-in) occurred in
neutron-irradiated specimens.
The changes in fracture mechanisms (change in cleavage triggering mechanism and
start of ductile crack growth) occurred in neutron-irradiated specimen at higher
temperatures than in non-irradiated specimens as expected from the DBTT shift obtained
from Charpy tests (see Fig. 1).
For quantitative fractographic analysis, the methodology developed in [3] was
adopted. The areas of different type of fracture in both irradiated and non-irradiated
specimens were measured from the images obtained using CCD camera and SEM. The
influence of neutron irradiation was observed. The dependence of fraction of ductile
fracture on temperature has the same character as the transition curve for energy absorbed
during the fracture process.
Correlation between energies obtained from instrumented Charpy tests and areas of
fracture surface was investigated. The energy absorbed before unstable crack initiation
( Wiu ) is closely correlated with ductile area (A) adjacent to the notch root (see Fig. 5).
The energy absorbed after crack arrest (KV � Wiu ) is correlated with the area of shear lips
and final shear fracture. The highest values of energy absorbed are best correlated with the
ductile area adjacent to the notch root, even if this area is comparable (in some cases even
smaller) with the other ductile areas (shear lips and final shear fracture). It can be
concluded that most energy is absorbed during the ductile crack growth from the notch
root. The correlations obtained were the same for irradiated and non-irradiated specimens.
The distribution of ductile dimple sizes on fracture surfaces of Charpy specimens
was determined using the image analysis. For image analysis, the micrographs obtained at
different magnifications ranging from �100 to �10,000 were used. The distribution of
dimple sizes was obtained for each magnification. Altogether 13,810 dimples were
identified. When the overlapping dimple size distributions determined at different
magnifications has been plotted all together, the total distribution seems to be continuous
in spite of the existence of two different distributions of the second phase particles
(inclusions and carbides), participating in ductile rupture. This result is in good agreement
with Goods and Brown [4]. It was found that the distribution of dimple sizes does not
change with increasing distance form the notch root, which probably means that the
mechanism of the ductile crack growth does not change with crack extension. It was also
found that irradiation has not influenced the distribution of ductile dimples (Fig. 6), which
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Š. Válek, P. Haušild, and M. Kytka
Fig. 5 Fig. 6
Fig. 5. The energy absorbed before initiation of unstable crack Wiu as a function of area of ductile
fracture adjacent to the notch root, A.
Fig. 6. Distribution of ductile dimples diameter on fracture surface of irradiated and non-irradiated
Charpy specimens.
24 2
probably means that the neutron irradiation (at least up to fluence 10 n�m � ) does not
change the mechanisms of ductile fracture.
Conclusions. The microstructure of 15Ch2MFA steel was characterized. The
15Ch2MFA steel contained two independent distributions of particles (MnS inclusions
and carbides).
The instrumented Charpy tests were performed on non-irradiated and neutronirradiated
specimens. The DBTT shift due to irradiation was about 50�C.
The fractographic analysis of broken Charpy specimens revealed the importance of
the ductile crack grow preceding the cleavage initiation. In non-irradiated specimens,
cleavage was triggered in cracked second phase particles or initiated in the vicinity of the
ductile crack tip. In neutron-irradiated specimens, cleavage initiated in areas where the
intergranular decohesion occurred.
The quantitative fractographic analysis showed the correlation of energy absorbed
before unstable crack initiation and the area of ductile fracture adjacent to the notch. It
was shown that most of the absorbed energy in the transition region belongs to the stage
preceding the cleavage crack initiation. The dependencies of the absorbed energy on the
ductile area were the same for irradiated and non-irradiated specimens. Moreover, the
distribution of ductile dimple sizes did not change with irradiation.
It can be concluded that irradiation has no apparent influence on the mechanisms and
24 2
kinetics of the ductile crack initiation and growth (at least up to fluence of 10 n�m � ).
Acknowledgment. This project has been financially supported by the Ministry of Education,
Youth, and Sports of the Czech Republic in the frame of the project No. MSM 6840770020.
1. Š. Válek, Physical Mechanism of Brittle Fracture in Low-Alloy Steels, Master Thesis, Czech
Technical University in Prague (2006), pp. 1–75.
2. P. Haušild, M. Kytka, M. Karlík, and P. Pešek, “Influence of irradiation on the ductile fracture
of a reactor pressure vessel steel,” J. Nucl. Mater., 341, No. 2-3, 184–188 (2005).
3. P. Haušild, I. Nedbal, C. Berdin, and C. Prioul, “The influence of ductile tearing on fracture
energy in the ductile-to-brittle transition temperature range,” in: Materials Science and
Engineering (2002), pp. 164–174.
4. S. H. Goods and L. M. Brown, “The nucleation of cavities by plastic deformation,” Acta
Metall., 27, No. 1, 71–85 (1979).
Received 28. 06. 2007
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UDC 539. 4
Compressive Creep of Fe3Al-type Iron Aluminide with Zr Additions
F. Dobeš, 1,a P. Kratochvíl, 2,b and K. Milièka 1,c
1
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech
Republic
2 Department of Metal Physics, Charles University, Prague, Czech Republic
a dobes@ipm.cz, b pekrat@met.mff.cuni.cz, c milicka@ipm.cz
High-temperature creep of a Fe3Al-type iron aluminide alloyed by zirconium was studied in the
temperature range 873–1073 K. The alloy contained (wt.%) 31.5% Al, 3.5% Cr, 0.25% Zr, 0.19% C
(Fe balance). It was tested in two states: (i) as received after hot rolling and (ii) heat treated (1423 K/
2 h/air). Creep tests were performed in compression at constant load with stepwise loading: in each
step, the load was changed to a new value after steady state creep rate had been established. Stress
exponent and activation energy of the creep rate were determined and possible creep mechanisms
were discussed in terms of the threshold stress concept. A rapid fall of the stress exponent and of the
threshold stress with the increasing temperature indicates that creep is impeded by the presence of
precipitates only at temperature 873 K. The results were compared with the results of long-term
creep tests in tension performed recently on the same alloy.
Keywords: iron aluminides, creep, threshold stress.
Introduction. Iron-aluminides-based alloys are promising candidates for many
industrial applications since they have excellent resistance to oxidation and sulfidation.
One of their drawbacks is the insufficient high-temperature strength. This can be
improved either through solid solution hardening or through precipitation hardening. The
alloying by additions of zirconium is expected to be effective in the precipitation
hardening due to low solubility and formation of phases (Fe, Al)2Zr and (Fe, Al)12Zr [1,
2]. This is in agreement with the review of existing studies of high temperature
mechanical properties of iron aluminides [3, 4], which documented that the addition of Zr
brings the best results. This fact initiated an investigation of quaternary alloy on Fe3Al
base with chromium and zirconium. The results of microstructural observations and of
tensile creep tests at 873 K were published elsewhere [5]. The aim of the present paper is
to report additional results of compressive creep tests of the same alloy performed in more
extensive range of temperatures and to start discussion of the potential rate-controlling
mechanisms.
Experimental. The composition of the alloy used for the experiment was as follows
(wt.%): Al = 31.5; Cr = 3.5; Zr = 0.25; C = 0.19; Fe – balance. The alloy was prepared in
the vacuum furnace and cast under argon in the Research Institute for Metals in Panenské
Bre�any, Czech Republic. The casting (dimensions 400�120�38 mm) was hot-rolled to
the final thickness of 13 mm at 1473 K in several steps with 20% reductions for each pass.
The rolled piece was heated after each second pass and the temperature did not decrease
under 1273 K during the total rolling period. After the final pass, the slab was quenched
from the temperature at least 1273 K into oil. One set of samples was additionally
annealed at 1423 K/2 h and air cooled.
The specimens for compressive creep tests were prepared with the axis
perpendicular to the rolling plane. The dimensions of samples were: diameter 4 mm,
height 12 mm. Constant load compressive creep tests of the alloy were performed at
temperatures from 873 to 1073 K. A stepwise loading was used: in each step, the load was
changed to a new value after steady-state creep rate had been established. The terminal
values of the true stress and the true strain rate were evaluated for the respective step.
© F. DOBEŠ, P. KRATOCHVÍL, K. MILIÈKA, 2008
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F. Dobeš, P. Kratochvíl, and K. Milièka
Protective atmosphere of dried and purified argon was used. During the test, temperature
was kept constant within �1 K. Creep curves were PC recorded by means of special
software. The sensitivity of elongation measurements was better than 10 5 � .
Results. The applied stress dependence of the minimum creep rate in the rolled
material is given in Fig. 1. The dependence can be described at a given temperature by the
power function
� ��A� ,
n
(1)
where A is a temperature dependent factor and n is exponent. The values of exponent n
are decreasing with increasing temperature: n� 12.2 at 873 K, 5.4 at 923 K, 4.9 at 973 K,
4.7 at 1023 K, and 4.6 at 1073 K. The apparent activation energy of creep can be obtained
from the Arrhenius-type plot (Fig. 2). It is about 433 kJ/mol at 50 MPa, 407 kJ/mol at 80
MPa, and 375 kJ/mol at 100 MPa at temperatures from 923 to 1073 K, respectively, but it
can be very high (greater than 700 kJ/mol) at lower temperatures.
Fig. 1 Fig. 2
Fig. 1. Applied stress dependence of creep rate at different temperatures.
Fig. 2. Dependence of creep rate on reciprocal absolute temperature.
An example of creep results obtained on samples after heat treatment is given in
Fig. 3. The heat treatment has positive effect on the creep resistance. The observed
deceleration of the creep rate is less than one order of magnitude. The results of previous
research of creep of the same alloy are also given in Fig. 3. A good coincidence of tensile
and compressive creep data can be admitted.
Discussion. The values of stress exponent n in Eq. (1) are usually taken as an
indication of potential creep controlling mechanisms. When dislocation motion controls
creep deformation of pure metals and single phase solid solutions, the exponent n of
about 3 to 5 is expected. The values of n can be substantially greater in alloys reinforced
with particles of secondary phases. The creep behavior is then rationalized by means of
the threshold stress concept: the stress dependence of the creep rate is rewritten as
�
A th n
� ���( ��� ) ,
where � th is the threshold stress. The value of exponent �
n should be close to the value
of n observed in pure metals and single phase solid solutions. The value of the threshold
stress can be determined in two different ways:
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(2)

Compressive Creep of Fe3Al-type Iron Aluminide ...
(i) The method based on the additivity rule [6]. It is necessary to know the behaviour
of corresponding single phase material.
(ii) The second method makes use of linearized plot of (� ) / 1 �
� n vs. applied stress.
The method is sensitive to the choice of stress exponent n �.
Fig. 3 Fig. 4
Fig. 3. Comparison of results of creep tests in tension and in compression.
Fig. 4. Dependence of threshold stress on temperature.
Fig. 5. Stress dependence of creep rate in present alloy and in two similar alloys from [8].
To enable a comparison with the previous application of the method to the results of
creep in Fe–Al alloys – and also the alloy with Zr addition from [8], we have used the
second method with the same value of n �,
i.e., n�� 4. The results are given in Fig. 4. Very
good agreement is obtained at temperature 873 K. The values of the threshold stress in the
present alloy are very rapidly decreasing with the increasing temperature and at
temperature 923 K and above they are substantially lower than the values reported in [8].
This fact, together with the above given values of stress exponent n, indicates that creep is
impeded by the presence of precipitates only at temperature 873 K. At temperatures
greater than 923 K it could be expected that either the precipitates have only minor
influence on the creep resistance of the investigated alloy or that they are dissolved. This
can be further documented by comparing present data with the data published in [8] for
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F. Dobeš, P. Kratochvíl, and K. Milièka
temperature 973 K (Fig. 5). The slope of the stress dependence of present alloy is lower
than that of the alloy Fe–20Al–Cr–Zr. Creep rates at low applied stresses are substantially
slower in Fe–20Al–Cr–Zr than in the present alloy. On the other hand, creep properties of
the present alloy are comparable with the properties of the binary alloy Fe–30Al without
second-phase precipitation.
CONCLUSIONS
1. The uniaxial compressive tests of Fe–31.5Al–3.5Cr alloy with 0.25 wt.% of Zr at
temperatures from 873 to 1023 K give the results comparable well with those of tensile
creep tests.
2. The values of stress exponent n, activation energy Q, and threshold stress indicate
a change of deformation mechanism within the above range of temperatures.
3. The applied amount of zirconium does not improve creep resistance efficiently at
temperatures above 873 K.
Acknowledgments. The paper is based on work supported by the Grant Agency of the Czech
Republic within the project 106/05/0409.
1. M. Palm, Intermetallics, 13, 1286 (2005).
2. F. Stein, M. Palm, and G. Sauthoff, Intermetallics, 13, 1275 (2005).
3. D. G. Morris, M. A. Muñoz-Morris, and J. Chao, Intermetallics, 12, 821 (2004).
4. D. G. Morris, M. A. Muñoz-Morris, and C. Baudin, Acta Mater., 52, 2827 (2004).
5. P. Kratochvíl, P. Málek, M. Cieslar, et al., Intermetallics, 15, 333 (2007).
6. R. Lagneborg and B. Bergman, Metal Sci., 10, 20 (1976).
7. R. W. Lund and W. D. Nix, Acta Metall., 24, 469 (1976).
8. D. G. Morris, M. A. Muñoz-Morris, and L. M. Requejo, Acta Mater., 54, 2335 (2006).
Received 28. 06. 2007
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UDC 539.4
Crack Growth in FeP04 Steel under Cyclic Tension for Different Notches on
the Basis of its Microstructure
D. Rozumek 1,a
1 Opole University of Technology, Department of Mechanics and Machine Design, Opole, Poland
a d.rozumek@po.opole.pl
We present the results of experimental work carried out in order to analyze the initiation and
propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under
cyclic tension by keeping constant the nominal load ratio R �0. Crack paths on the basis of the
tested material microstructure were observed.
Keywords: crack path, microstructure, fatigue crack growth rate, notches, J-integral range.
Introduction. In steels and alloys, two basic crack growth mechanisms can be
distinguished: brittle and ductile [1]. In case of brittle cracking, intercrystalline cracking
(so-called fissile cracking) is usually observed. For ductile cracking, disintegration of the
specimen surface in pure metals is caused by successive slip bands; in commercial alloys
cracking begins in harder elements (non-metallic inclusions), where the developing voids
cause failure. During fatigue crack growth in metal alloys, the following three stages can
be distinguished [2]. The first stage includes generation of microcracks or formation of
voids and is connected with phenomena occurring in the dislocation structure of the
material. The second stage includes crack growth in the plane of maximum principal
stresses. The final fracture causes the growing crack to reach its critical length, or the
stress reaches the tensile strength level, and the element fails.
The aim of this study is determination of the fatigue crack growth in FeP04 steel,
used in car industry, taking into account the influence of microstructure and different
notches on the steel life (fatigue crack growth rate).
Materials and Test Procedure. Static Properties and Fatigue Tests of Notched
Specimens. Tests were carried out on plates made of FeP04-UNI 8092 deep-drawing steel,
weakened by symmetric lateral notches of varying acuity. The tests were performed using
a MTS 809 servo-hydraulic device at the Department of Management and Engineering in
Vicenza (Padova University) [3]. Chemical composition (wt.%) of the FeP04 steel tested
are 0.05 C, 0.30 Mn, 0.05 Si, 0.032 P, 0.02 S, 0.043 Al, and 0.07 Cu. Mechanical
properties of FeP04 steel are as follows: � y � 210 MPa, � u � 330 MPa, E � 191 GPa,
��03 . .Coefficients of the Ramberg–Osgood equation describing the cyclic strain curve
under tension–compression conditions with R� ��1 for FeP04 steel are the following
[4]: the cyclic strength coefficient K �� 838 MPa and the cyclic strain hardening exponent
n�� 022 . . All fatigue tests were performed under force control, by imposing a constant
value of the nominal load ratio R � 0 with load amplitudes Pa � 6 and 7 kN (which
corresponded to the nominal amplitude of normal stresses � a � 100 and 117 MPa before
the crack initiation). The test frequency ranged from 13 to 15 Hz. The specimens were
characterized by double symmetric lateral notches with a notch root radius ranging from
0.2 mm to 10 mm (Fig. 1). The theoretical stress concentration factor in the specimen
under tension K t � 961 . ,4.30, 3.23, and 1.85 was estimated with use of the model [5]. In
a number of fatigue tests, fatigue crack initiation and propagation phases were controlled
by means of an optical microscope (�20).
Microstructure and Fatigue Crack path in FeP04 Steel. Steel FeP04 can be easily
subjected to cold working, it belongs to ferritic steels. Since amount of carbon in ferrite is
low, ferrite properties are very similar to those of pure iron �. The considered steel is
© D. ROZUMEK, 2008
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D. Rozumek
applied for deep drawing. Fig. 2b shows microstructure of FeP04 steel, containing the
ferrite (light) and numerous non-metallic inclusions. The structure exhibits a distinct
rolling texture. Numerous non-metallic inclusions, mainly chains of oxides about 1 �m
(black) are visible against the background of long ferrite grains. The coalesced cementite
can be seen at the ferrite grain boundaries in Fig. 2b. Figure 2 presents the surface of a
specimen tested under loading Pa � 6 kN and with the radius of notch root �� 02 . mm
after N f � 22, 700 cycles to failure. Different magnifications were chosen so as to present
a path of the main crack, about 0.9 mm in length (Fig. 2a). Figure 2b shows a crack course
taken from Fig. 2a, for magnification �2000, in order to analyze the crack growth. Here,
transcrystalline cracks through the grains of �-phase are dominating, but cracks along the
grain boundaries are also observed. The main cracks propagate in direction perpendicular
to the loading action, but secondary cracks are also visible.
Fig. 1. Geometry of the specimen characterized by notches.
a b
Fig. 2. The fatigue crack path in the FeP04 steel, magnification: (a) �200; (b) �2000.
Initiation and growth of short (secondary) fatigue cracks can be seen in grains or at
the boundaries of �-phase (Fig. 2b). In most cases, the secondary cracks growing in the
ferrite grains are blocked in the places where coalesced cementite and the non-metallic
inclusions are present. Further characteristic of the considered cracks, including short
cracks, is that they grow in different directions in relation to the specimen axis. The main
cracks grow in the planes of the maximum normal stresses. There are short lateral cracks
inclined to the main crack at the angle of 30 and 40�. Because of high plasticity of the
tested material, ductile cracking is observed. It is characterized by voids (black fields in
Fig. 2) after the material stratification observed in the cracking path. Stress concentration
and intensification of plastic flow occur around the voids. In Fig. 2a, asymmetric pits can
be found, which are caused by the mean loading and located in the perpendicular plane or
at a certain angle (up to 30�) to direction of the external loading action. Stratification of
the material can be seen at a certain distance from the main crack. The fatigue crack
growth rate in the ferrite grains is dependent on the stress value. Similar crack growth was
observed in case of specimens with the notch root radii ��125 . , 2.5, and 10 mm.
Test Results and Analysis. In double logarithmic coordinates, Fig. 3 gives the
number of cycles to initiation and to failure for different notch root radii. The cracks (of
minimal observable crack length about 0.1 to 0.2 mm) initiated at the same time on the
left and on the right of the slot. As seen from curves crack length a vs number of cycles
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N in Fig. 4, after changing the notch root radii � from 0.2 to 10 mm, fatigue life
increases. It is evident that with the highest radii, the initiation phase, which depends on
the stress conditions at the notch tip, prevails.
On the basis of the results presented in Figs. 3 and 4 it can be stated that with the
increase of notch root radii the number of cycles to initiation and failure of specimens also
rises. Fig. 5a shows the fatigue crack growth rate da dN versus �K relations under
different notch root radii and load amplitude conditions. For different notches, under
Pa � 7 kN, with the notch radius change (from �� 1.25 to ��10 mm in the range
76��K�100 MPa�m 12 / ) the crack growth rate increases. Figure 5b shows the fatigue
crack growth rate da dN versus �J relations. These relations show almost the same
tendency as the da dN versus �K relations. In Fig. 5 and for �� 0.2 and 10 mm, at the
initial stage of the crack growth, there is the influence of plasticity visible (displacement
of symbols � to the right in relation to symbols �).
In the elastic-plastic range, stresses and strains were calculated by means of the finite
element FRANC2D software. In the models six-node triangular elements were used. The
test results shown in Fig. 5a were described by the Paris equation [6] and in Fig. 5b by the
modified equation
da dN B K n
� ( � ) and da dN B J n
( � ) 1 ,
(1)
� 1
where �J�J max �J
min , B B , 1 and n n , 1 are empirical coefficients. The �J value in
Eq. (1) was calculated by using the following relationship [7], which is for slightly
hardening and cyclically stable materials
2
�K
�J
� ��Y
E
Crack Growth in FeP04 Steel under Cyclic Tension ...
Fig. 3 Fig. 4
Fig. 3. Comparison between crack initiation points (open symbols) and final failures (solid
symbols), as a function of different values of the notch root radius.
Fig. 4. Dependencies of fatigue crack length versus number of cycles for different values of the
notch root radius.
2
���� n�
p
a,
(2)
where �K�K max �K min �Y�� �( a�a0) and �� is the stress range corresponding
to the plastic strain range �� p , both ranges evaluated ahead of the notch (stress and strain
fields by FEM for slot were calculated the near crack tip about 0.1 to 0.5 mm – local
approach), a0 is notch depth, Y is correction factor [4], Y �112 . �0203 . ( 2( a�a0) w)
�
2
3
1197 . ( 2( a�a0) w) �193 . ( 2(
a�a0) w)
, and w is specimen width. The empirical
coefficients B, B1and
n n , 1 occurring in Eq. (1) and the correlation coefficients r were
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D. Rozumek
Table 1
Coefficients B and n in Eq. (1) and Correlation Index r for the Curves in Fig. 5
Figures,
graphs
B,
m ( MPa m)
,
n cycle
n r B1 ,
n
m ( MPa m)
1, cycle
5a-1, 5b-1 2 377 10 10
. � � 1.808 0.89 1950 10 6
. � � 0.453 0.89
5a-2, 5b-2 1722 10 12
. � � 2.954 0.82 2 636 10 6
. � � 0.467 0.87
5a-3, 5b-3 3 069 10 14
. � � 3.802 0.94 5 346 10 6
. � � 0.889 0.94
5a-4, 5b-4 2 917 10 9
. � � 1.166 0.74 1050 10 6
. � � 0.304 0.80
a b
Fig. 5. Crack growth rate behavior da dN versus �K (a) and da dN versus �J (b).
determined with the least square method for a confidence level �� 005 . and they were
shown in Table 1.
Conclusions. In the considered material, ductile cracking is observed and in such
cracking voids occur after material lamination. At the specimen fractures, it was possible
to find transcrystalline cracks through the grains of �-phase and cracks along the grain
boundaries. The notch root radius rises together with increase number of cycles to
initiation and failure of specimens. After comparison of the influence of notches with
�� 0.2 and 10 mm on the crack growth rate, at the initial cracking period larger plastic
were observed for �� 0.2 (see displacement of symbols in Fig. 5).
1. S. Kocanda, Fatigue Failure of Metals, Sijthoff & Noordhoff Int. Publishers (1985), p. 441.
2. D. Rozumek amd E. Macha, A Description of Fatigue Crack Growth in Elasto-Plastic
Materials under Proportional Bending with Torsion [in Polish], Opole University of
Technology (2006), p. 198.
3. P. Lazzarin, R. Tovo, and G. Meneghetti, Int. J. Fatigue, 19, 647–657 (1997).
4. D. Rozumek, E. Macha, P. Lazzarin, and G. Meneghetti, J. Theor. Appl. Mech., 44, 127–137
(2006).
5. A. Thum, C. Petersen, and O. Swenson, Verformung, Spannung, und Kerbwirkung, VDI
(1960).
6. P. C. Paris and H. Tada, Int. J. Fracture, 11, 1070–1072 (1975).
7. D. Rozumek, Proc. 12th Int. Conf. on Experimental Mechanics (ICEM12), Politecnico di Bari
(2004), pp. 275–276.
Received 28. 06. 2007
124 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1
n 1
r 1

UDC 539. 4
Estimation of Anisotropy of Mechanical Properties in Mg Alloys by Means of
Compressive Creep Tests
F. Dobeš, 1,a P. Pérez, 2,b K. Milièka, 1,c G. Garcés, 2,d and P. Adeva 2,e
1
Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno, Czech
Republic
2 National Center of Metallurgical Investigations, Madrid, Spain
a dobes@ipm.cz, b zubiaur@cenim.csic.es, c milicka@ipm.cz, d ggarces@cenim.csic.es,
e adeva@cenim.csic.es
A detailed knowledge of dependence of mechanical properties on orientation in materials prepared
by directional processes may present an important factor influencing the design of construction
parts. Toward this end, the compressive creep testing of short specimens may be useful. Three
different magnesium-based materials were subjected to this testing: (i) pure magnesium, (ii)
magnesium matrix composite reinforced with 10 vol.% of titanium, and (iii) magnesium alloy WE54.
All three materials were prepared through a powder metallurgical route with final hot extrusion.
The specimens for creep tests were cut in such a way that their longitudinal axis (i.e., the direction
of compressive creep stress) and the axis of extruded bar contained a predestined angle. Two
extreme cases can be observed: In pure Mg and in Mg–Ti composite, the dependence of the creep
rate is very sensitive to the orientation especially at small inclinations from extrusion axis. The
greatest creep resistance is observed in specimens with stress axis parallel to the extrusion axis, the
lowest at declinations from 45 to 90�. On the other hand, in WE54 no orientation dependence was
observed. Possible explanations of the behaviour based on microstructural observations are
discussed.
Keywords: magnesium, creep, composite, texture.
Introduction. Microstructure of many materials – either intentionally or owing to
production history – is not isotropic. Consequently, mechanical properties are not
isotropic, too. A detailed knowledge of dependence of these properties on orientation
within material may be important for an exact design of construction parts. An investigation
of orientation dependence may also contribute to identification of mechanisms that control
the respective property. The anisotropy of mechanical properties is important in hexagonal
metals and alloys, especially in light-weighted magnesium alloys and a great attention has
been recently devoted to its study [1–6]. We present the results of orientation dependence
of creep properties of magnesium-based alloys prepared by powder metallurgical
processing.
Experimental. Commercially pure magnesium powder with a particle size less than
45 �m and grain sizes ranging between 1 and 8 �m, was cold-pressed at 310 MPa
pressure level, leading to a densification of around 95%. The compacts were hot-extruded
into rods at 673 K using an extrusion ratio of 18:1.
A magnesium matrix composite reinforced with 10 vol.% of titanium particles was
prepared from the same magnesium powder as the previous material and from the
titanium powder of particle size less than 25 �m. The powders were mixed for 3hat100
rpm in a planetary mill. The next technology steps were identical with those for the pure
magnesium material: cold-pressing at 310 MPa and hot-extrusion into rods at 673 K using
an extrusion ratio of 18:1.
The third investigated material was the magnesium-based alloy WE54 alloy. The
alloy contained 5 wt.% of Y, 2 wt.% of Nd, and 2 wt.% of rare earth elements. The
powder prepared by rapid solidification had size less than 100 �m. The powder was
© F. DOBEŠ, P.PÉREZ, K. MILIÈKA, G. GARCÉS, P. ADEVA, 2008
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F. Dobeš, P.Pérez, K. Milièka, et al.
cold-pressed by slowly increasing pressure up to 340 MPa in a special die designed for
this purpose. The resulting compacts of 40 mm in diameter were extruded at 673 K
employing an extrusion ratio of 20:1.
Results of the subsequent characterization of materials by optical microscopy,
scanning electron microscopy, X-ray diffraction and tensile tests are given elsewhere
[7–9].
Cylindrical specimens of diameter 5 mm and height 9 mm were prepared by
spark-cutting from the extruded bars. The specimens were cut in such a way that their
longitudinal axis (i.e., the direction of compressive creep stress) and the axis of extruded
bar contained a predestined angle from 0 to 90�. Constant load compressive creep tests of
the alloy were performed at temperatures from 523 to 623 K. A stepwise loading was
used: in each step, the load was changed to a new value after stationary creep rate had
been established. The terminal values of the true stress and the true strain rate were
evaluated for the respective step. Protective atmosphere of dried and purified argon was
used. During the test, temperature was kept constant within �1K. Creep curves were PC
recorded by means of special software. The sensitivity of elongation measurements was
better than 10 5 � .
Results. Examples of experimental dependences of the creep rate �� on the applied
stress � for different orientations of specimens are given in Figs. 1–3. Two basic patterns
of behavior can be observed: In pure Mg and in Mg–Ti composite, the dependence of the
creep rate is very sensitive to the orientation especially at small inclinations from
extrusion axis. The highest creep resistance is observed in specimens with stress axis
parallel to the extrusion axis, while the lowest resistance is at declinations from 45 to 90�.
A more exact determination of orientation with the lowest creep resistance is complicated
by the scatter of experimental data. On the other hand, in WE54 no orientation
dependence is observed. Another feature that distinguishes two groups is the dependence
of creep rate on the applied stress. The dependences can be formally described by the
power function
� ��A� ,
n
(1)
where A is a temperature dependent factor and n is exponent. The values of exponent n
are about 19 in pure Mg and from 20 up to 32 in Mg–Ti composite. Relatively high values
of n are typical for creep in metallic materials strengthened by dispersion of secondary
phase. In the alloy WE54, the stress exponent n is about 4 for all orientation.
Fig. 1 Fig. 2
Fig. 1. Dependence of creep rate on applied stress in Mg.
Fig. 2. Dependence of creep rate on applied stress in Mg–Ti composite.
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Estimation of Anisotropy of Mechanical Properties in Mg Alloys ...
Fig. 3 Fig. 4
Fig. 3. Dependence of creep rate on applied stress in WE54.
Fig. 4. Dependence of creep rate on orientation of samples in Mg and in Mg–Ti composite.
The equation (1) was used also for an evaluation of the influence of orientation on
the creep rate. The creep rates corresponding to the applied stress 40 MPa were calculated
by means of optimized values of A and n for all orientations. The results are given in
Fig. 4.
Discussion. Microscopic observations revealed three distinct anisotropic features of
the structure of alloys: (i) elongated grains, (ii) crystallographic texture and (iii) elongated
oxide and titanium particles.
(i) Grains in Mg–Ti are elongated in the extrusion direction, with an aspect ratio of
about 2. It is generally accepted that the grain size and shape influences the rate of
diffusional creep but not the rate of dislocation creep [10]. The diffusional creep can be
excluded as possible rate-controlling mechanism due to the observed high values of stress
exponent. At any rate, following the original formulation of volume diffusion controlled
creep rate [11], the creep rate in specimens perpendicular to extrusion direction should be
faster than in parallel direction by a factor about square root of grain aspect ratio, which is
considerably less than observed experimentally.
(ii) Pure magnesium and Mg–Ti composite exhibited a fiber texture with the basal
planes parallel to the extrusion direction. For such a type of texture, the slip motion of
dislocations in the extrusion direction should be the easiest. In addition to this, deformation
behavior is influenced by values of the resolved shear stress on the respective slip planes
and by activities of other deformation mechanism and slip systems. At room temperature,
it was shown that the yield stress is the lowest for tension parallel to extrusion axis and it
was ascribed to possibility of twinning. However, at elevated temperatures, twining tends
to be inhibited and this fact leads to strong texture strengthening, especially if the test
temperature is not high enough for the activation of non-basal slip systems.
(iii) Titanium particles in Mg–Ti composite are very often highly deformed; they are
elongated in the extrusion direction to such an extent that they can be considered as long
fibres. Their existence seems to be another plausible reason for an explanation of the
observed creep behavior [12]. Similar mechanism has to be taken into account also in
pure-magnesium material due to its powder-metallurgical processing, since the grains
elongated in the extrusion direction are decorated by oxide particles. These particles come
from the fracture during the extrusion of the oxide film which covers the original
magnesium powders.
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F. Dobeš, P.Pérez, K. Milièka, et al.
The negative effect of specimen tilt on creep resistance in WE54 can be related to a
randomization of grain orientation. Since the deformation texture should not be very
distinct from other magnesium alloys, it is thus probable that the resulting texture is
influenced by recrystallization. This effect is associated with nucleation of recrystallization
stimulated by second-phase particles [13, 14] and can have a positive importance for
ensuing technological processes.
Acknowledgments. The financial support of the Grant Agency of the Czech Republic within the
project 106/06/1354 is gratefully acknowledged. The paper was prepared within the joint research
program of the Spanish National Research Council CSIC and the Academy of Sciences of the Czech
Republic.
1. H. Somekawa and T. Mukai, Scripta Mater., 53, 541 (2005).
2. L. Helis, K. Okayasu, and H. Fukutomi, Mater. Sci. Eng. A, 430, 98 (2006).
3. J. A. del Valle and O. A. Ruano, Acta Mater., 55, 455 (2007).
4. D. K. Xu, L. Liu, Y. B. Xu, and E. H. Han, Mater. Sci. Eng. A, 443, 248 (2007).
5. G. Garcés, M. Rodríguez, P. Pérez, and P. Adeva, Composit. Sci. Technol., 67, 632 (2007).
6. J. Bohlen, M. R. Nurnberg, J. W. Senn, et al., Acta Mater., 55, 2101 (2007).
7. P. Pérez, G. Garcés, and P. Adeva, J. Mater. Sci. (in print).
8. P. Pérez, G. Garcés, and P. Adeva, Composit. Sci. Technol., 64, 145 (2004).
9. G. Garcés, M. Maeso, P. Pérez, and P. Adeva, Mater. Sci. Eng. A (in print).
10. J. P. Poirier, Plasticité à Haute Température des Solides Cristallins, Editions Eyrolles, Paris
(1976).
11. C. Herring, J. Appl. Phys., 21, 437 (1950).
12. F. Dobeš, P.Pérez, K. Milièka, et al., in: K. Kainer (Ed.), Proc. of the 7th Int. Conf. on
Magnesium Alloys and Their Application, WILEY-VCH, Weinheim, FRG (2007), p. 699.
13. E. A. Ball and P. B. Prangnell, Scripta Metall. Mater., 31, 111 (1994).
14. G. W. Lorimer, L. W. F. Mackenzie, F. J. Humphreys, and T. Wilks, Mater. Sci. Forum,
467–470, 477 (2004), 488–489, 99 (2005).
Received 28. 06. 2007
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UDC 539. 4
Duplex Surface Treatment of Stainless Steel X12CrNi 18 8
J. Kadlec 1,a and M. Dvorak 2,b
1 Department of Mechanical Engineering, University of Defence in Brno, Brno, Czech Republic
2
Department of Mechanical Technology, Faculty of Mechanical Engineering, Brno University of
Technology, Brno, Czech Republic
a b
jaromir. kadlec@unob.cz, dvorak.m@fme.vutbr.cz
Described technology of stainless steel duplex surface treatment is based on the plasma nitriding of
the component in micropulse plasma and subsequent coating by Ni and composite Ni/diamond film.
The formed duplex coating is characterized by very good mechanical properties, e.g., an excellent
abrasion resistance, a low friction coefficient and a high hardness.
Keywords: plasma nitriding of stainless steel, chemical composition, structure, properties.
Experimental. Duplex coating technology is based on combination of both plasma
surface treatment (ion nitriding) and subsequent deposition of thin film [1, 2]. In this case,
the plasma nitrided layer was either electroplated by nickel film or electroplated by
composite Ni/diamond film (Watts bath) containing codeposited diamond particles with
average particle size of 0.5 �m in diameter. Thickness of electroplated films reached units
of micrometers. Steel X12CrNi 18 8 (1.4300) widely used in food-processing industry and
in medicine for surgical instruments was applied for experiment. Chemical composition
according to DIN standard, measured by GDOES method and verified for selected
chemical elements by EDS method is presented in Table 1. Plasma nitriding process was
carried out on the PN 60/60 equipment according to parameters given in Table 2. For
experiment two samples were used. Parameters of subsequent coating process are listed in
Table 3.
Table 1
Chemical Composition of Stainless Steel X12CrNi 18 8
Method Chemical Composition (wt.%)
C Mn Si Cr Ni P S Al
DIN standard �0.12 �2.00 �1.00 17–19 8–10 �0.045 �0.030 –
GDOES/Bulk 0.045 1.78 0.45 18.6 8.60 0.027 0.002 –
EDS – – 0.58 18.9 8.45 – – 0.39
Notes: Parameters of GDOES/Bulk analysis: U � 1002 V, I � 34.9 mA, p Ar � 450 Pa. Parameters
of EDS analysis: U � 30 kV, M ��250, I � 134 pA, WD � 21.20 mm.
Chemical composition of substrate alloy was measured by GDOES/Bulk method
(SA 2000 spectrometer) and by EDS method (Noran system Six), depth profiles was
evaluated by GDOES/QDP and EDS methods. Calibration of nitrogen: JK41-1N and
NSC4A standards. Microstructure and surface morphology was evaluated by electron and
light microscopy (Vega TS 5135 electron microscope and Neophot 32 light microscope),
respectively. Surface structure was tested by the 3D topography method (TALYSURF CLI
1000) with confocal gauge CLA before and after treatment. Layer thickness and microhardness
were measured by indentation method (M400 microhardness tester). From
microhardness behavior the layer depth in accordance with DIN 50 190 standard as Nht
© J. KADLEC, M. DVORAK, 2008
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J. Kadlec and M. Dvorak
Table 2
Parameters of Plasma Nitriding Process
Parameter Plasma cleaning Plasma nitriding
(sample 3.4)
Plasma nitriding
(sample 3.2)
Temperature (�C) 520 450 550
Time/Duration (min, h) 30 min 8 h 8 h
Flow H2 (l/min) 20 8 8
Flow N2 (l/min) 2 32 32
Flow CH4 (l/h) 0 1.5 1.5
Voltage (V) 800 530 530
Pulse length (�s) 100 100 100
Pressure (Pa) 80 280 280
Table 3
Parameters of Subsequent Coating Process
Coating Temperature (�C)/
Duration (min)
Current density
(mA/cm 2 )
Diamond particles
(wt.%)
Nickel 60/5 10–15 –
Nickel/diamond 60/5 10–15 6–10
parameter was determined. Other properties (adhesion, corrosion resistance) were evaluated,
too. Relations among chemical composition, structure and diffusion layer properties were
briefly discussed.
Results and Discussion. Depth profiles of plasma nitrided layers (Figs. 1 and 2) for
both carbon and nitrogen are in good agreement with the proposed plasma treatment
regimes. Carbon and nitrogen contents decrease along the layer depth (from surface to
substrate). As for carbon concentration there is local maximum ten micrometers from the
surface. Existence of this maximum was verified by microstructure evaluation, too.
Fig. 1. Chemical composition (sample 3.4). Fig. 2. Chemical composition (sample 3.2).
130 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Duplex Surface Treatment of Stainless Steel X12CrNi 18 8
A very sharp interface between substrate material and plasma nitrided layer was found
out (Figs. 3 and 4). Thickness/depth of plasma nitrided layer was evaluated by way of
microhardness behavior measurement in compliance with DIN 50 190 standard. Attained
Nht value is Nht 270 HV 0.05 = 0.08 mm (Fig. 4). This result is in conformity with
spectrometric and metalographic measuring and evaluation. The highest value of measured
microhardness was observed for plasma nitrided layer of sample 3.2 and reached 1578
HV 0.05.
Fig. 3 Fig. 4
Fig. 3. Microstructure of sample 3.2 (Vilella Bain).
Fig. 4. Microhardness behavior of sample 3.2 (determination of layer depth).
Results of surface morphology of Ni/diamond coating evaluation, indentation adhesion
test of plasma nitrided layer (is equal to HF1–HF2) and Calotest of Ni coating,
respectively, are in Figs. 5–7.
Fig. 5 Fig. 6
Fig. 7
Fig. 5. Surface morphology of Ni/diamond composite.
Fig. 6. Indentation adhesion test (plasma nitrided layer).
Fig. 7. Result of thickness measurement – Calotest.
Qualitative and quantitative results of 3D surface topography measurements are
shown in Figs. 8 and 9. The most important parameters of surface structure are presented
at the same time.
Conclusions. Plasma nitrided layer on the steel X12CrNi 18 8 surface at two
different temperatures with subsequently deposited Ni based films was carried out. The
focus was on the relations between chemical composition, structure and properties of the
formed coatings. It follows from GDOES measurements that a variable composition depth
profile can be fabricated. The highest value of microhardness 1578 HV 0.05 was observed
for plasma nitrided layer (550�C/8 h). To restore surface corrosion resistance, two types of
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J. Kadlec and M. Dvorak
Fig. 8. 3D surface topography (sample 3.2, plasma nitriding 550�C/8 h): P a � 0.345 �m; P q �
0.452 �m; P t � 2.83 �m; R a � 0.358 �m; R q � 0.47 �m; R t � 2.73 �m; W a � 0.043 �m;
W q � 0.0512 �m; W t � 0.168 �m.
Fig. 9. 3D surface topography (sample 3.4, plasma nitriding 450�C/8 h): P a � 0.373 �m; P q �
0.469 �m; P t � 2.93 �m; R a � 0.375 �m; R q � 0.477 �m; R t � 2.75 �m; W a � 0.0265 �m;
W q � 0.0298 �m; W t � 0.114 �m.
highly adhesive electrolytic nickel-based thin films with thickness in units of micrometers
were subsequently deposited. These thin films improve not only corrosion resistance, final
surface structure and surface mechanical properties, but also perfect the appearance of
treated surface.
Acknowledgements. The work was supported by research project BTU Brno BD13713313
and by Ministry of Defence of the Czech Republic, project No. FVT 0000404.
1. J. Kadlec, V. Hruby, and M. Novak, Vacuum, 41, 2226 (1990).
2. W. S. Baek, S. C. Kwon, J. J. Rha, et al., Thin Solid Films, 429, 174 (2003).
Received 28. 06. 2007
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UDC 539. 4
Microstructural and Fracture Analysis of Aged Cast Duplex Steel
D. Dyja, 1,a Z. Stradomski, 1,b and A. Pirek 1,c
1 Czestochowa University of Technology, Institute of Materials Engineering, Czestochowa, Poland
a dyjad@mim.pcz.czest.pl, b zbigniew@mim.pcz.czest.pl, c pireka@mim.pcz.czest.pl
The effect of increased carbon content and heat treatment parameters on the microstructure and
selected properties of ferritic-austenitic duplex cast steel is discussed. Test results show that the cast
steel microstructure after the solution heat treatment changes substantially with increasing carbon
content. Ageing after the solution heat treatment results in approx. 20% increase in hardness and a
few-times decrease in impact strength. Fractographic examinations show that fracture surfaces of
specimens of steel with low carbon content are typically of transcrystalline ductile micromechanism.
An increase in carbon content is accompanied by a decline in ductility areas, while fracture of
specimens is of mixed nature: ductile and brittle. After ageing, only cases of mixed fracture were
observed.
Keywords: duplex cast steel, heat treatment, brittle fracture, carbides, impact energy.
Introduction. Chemical composition of cast alloyed duplex steels is selected, in
order to ensure the required properties via appropriate amount of ferrite and austenite in
the microstructure. However, depending on the chemical composition, conditions of
thermal treatment and manufacturing technology intermetallic phases (�, �, �,
R) and
carbides can cause increase of brittleness and reduction of corrosion resistance [1, 2]. As
observed in literature and shown in numerous advertising materials of casting companies
this is promoted by the trend to increase the carbon content above the value most often
presented in standards (C max � 0.03%). Higher carbon content facilitates the handling of
metallurgical process (in particular, in casting shops which do not have secondary
metallurgy) and has a favourable effect on erosion resistance of duplex cast steels [3, 4].
However, an increased carbon content creates qualitative problems related both to the
solidification course and processes during cooling of the casing in the solid state, what has
been described in detail in [5, 6].
Despite technological difficulties related to casting propensity for cracking, the
optimum combination of mechanical properties with erosion wear resistance makes that
the demand for this material permanently increases, especially for the components
operating in environment of liquid solutions heavily polluted with solid particles [7].
Erosion-corrosion influence of such environment is the reason of costly breakdowns and
down times caused by premature wear of components. This applies, in particular, to
components of dewatering sets including mainly pump impellers, sleeves or elements of
pipelines [8]. This problem is resolved, among others, by the use of high-alloy Fe–Cr–Ni
cast steels containing addition of 3–4% of copper, which increases resistance to acid
action and ensures obtaining of precipitation hardening by �-Cu phase as a result of ageing
at 480�C [9]. The aim of this study was determination of the effect of increased carbon
content on selected mechanical and plastic properties of the solution heat-treated and aged
duplex cast steel.
Materials and Methodology. The chemical composition (in mass %) of the
ferritic-austenitic duplex cast steels used for the present work is listed in Table 1. The cast
steel was solution heat-treated in water after two-hour soaking at 1080�C and then aged at
480�C for 4 hours. Specimens for optical metallography (OM) were chemically etched in
a 30 g potassium ferricyanide + 30 g potassium hydroxide + 60 ml distilled water.
Hardness was measured by the Brinell method under a load of 1838 N with a steel ball of
© D. DYJA, Z. STRADOMSKI, A. PIREK, 2008
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D. Dyja, Z. Stradomski, and A. Pirek
a diameter of 2.5 mm. Charpy impact energy was measured on Charpy V specimens at
ambient temperature on a hammer of an initial energy of 300 J. Fractography of the
broken specimens was performed in a JEOL JSM 5400 scanning electron microscope.
Table 1
Chemical Composition of Examined Cast Steels
Heat No. C Cr Ni Cu Mo Mn N Si S P
1 0.028 24.20 8.82 0.02 2.30 0.46 0.068 0.85 0.010 0.011
2 0.040 24.70 6.74 3.11 2.22 0.88 0.140 0.88 0.012 0.017
3 0.055 24.40 6.71 3.08 2.40 0.14 0.085 0.81 0.020 0.020
4 0.060 24.70 6.91 3.00 2.90 0.14 0.078 0.73 0.018 0.019
5 0.090 24.00 8.02 2.60 2.25 0.24 0.080 1.05 0.010 0.016
6 0.120 25.00 6.95 2.85 2.56 0.19 0.075 0.90 0.030 0.020
Results. Examples of the steel microstructure after the solution heat treatment from
1080�C/2 h/water are presented in Fig. 1. Cast steels from heat 1–3, containing C max �
0.055% feature a two-phase ferritic-austenitic microstructure with austenite grains
distributed in the ferritic matrix (Fig. 1a).
Fig. 1. Microstructure of the cast steel: (a) heat 1; (b) heat 4; (c) heat 6, after 1080�C/2 h/water.
A carbide eutectic (Fig. 1b and 1c), non-dissolved during the heat treatment, is
observed in the microstructure of solution heat-treated cast steel with increased carbon
content (heat 4–6); its volume fraction increases from VE � 0.03% (0.06% C for heat 4)
to VE � 2.00% (0.12% C for heat 6) with carbon content increasing. Effects of ageing at
480�C in the microstructure changes are not visible via optical microscopy. However, as a
result of isothermal holding at this temperature, a spinodal decomposition of ferrite occurs
(with creation of � phase, enriched in iron, and chromium-rich �� phase) as well as
precipitation in the ferrite of copper-rich �-Cu phase.
Results of measurements of the steel hardness and impact energy after ageing
specified in Table 2 show a small, about 20%, increase in hardness as compared to the
solution heat-treated material with simultaneous clear decline in impact energy. General
increase in the steel hardness after ageing is affected mainly by the increase in ferrite
microhardness related to spinodal decomposition into � and �� phase as well as to
precipitation of copper-rich �-Cu phase. Noteworthy is very unfavourable influence of
increased carbon content on cast steel impact energy. As shown in Table 2, the impact
energy of cast steel containing 0.028% carbon (heat 1) after solution heat treatment has to
160 J and falls to 10 J for cast steel containing 0.12% carbon (heat 6). The ageing at
480�C, causing a slight increase in hardness, results in a clear few-times decrease in the
impact energy as compared to solution heat-treated cast steel.
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Microstructural and Fracture Analysis of Aged Cast Duplex Steel
Table 2
Results of Hardness, Microhardness, and Impact Energy of Investigated Steels
Process Heat 1 Heat 2 Heat 3
HB KV HV � HV � HB KV HV � HV � HB KV HV � HV �
Solutioning 215 160 335 205 245 148 353 216 242 142 350 214
Ageing 259 58 420 210 279 55 434 232 285 50 437 233
Heat 4 Heat 5 Heat 6
HB KV HV � HV � HB KV HV � HV � HB KV HV � HV �
Solutioning 251 118 348 230 258 38 351 228 266 10 355 240
Ageing 298 28 439 260 307 19 445 239 313 6 450 248
Note. Values of HV � and HV � correspond ferrite and austenite microhardnesses, respectively.
To explain microstructural origins of changes in mechanical properties, selected
fracture surfaces of broken impact test specimens were subjected to fractographic analysis
using SEM. The examples of fracture surfaces observed are presented in Figs. 2 and 3.
Fig. 2. SEM microphotographs of the steel: (a) heat 1; (b) heat 6; after 1080�C/2 h/water.
Fig. 3. SEM microphotograph of the investigated steel after the ageing (heat 1).
For the steels with low carbon content after the solution heat treatment characteristic
ductile fracture is observed (Fig. 2a) and sulphide inclusions, most often of spheroidal
shape, have been revealed on fracture surfaces. An increase in carbon content in the cast
steel is accompanied by a decline in ductility areas, specimen fractures are of mixed
ductile and brittle nature (Fig. 2b). Morphology of specimen fracture is subject of
significant change after ageing. Two mechanisms of cracking are observed on the
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D. Dyja, Z. Stradomski, and A. Pirek
surfaces: transcrystalline cleavage and ductile, the former one prevailing. A typical
example of mixed fracture is presented in Fig. 3. Numerous faults and changes of cracking
surfaces and only a few traces of ductile cracking exist in elementary interfaces.
Conclusions
1. The cast steel structure after the solution heat treatment changes substantially with
increasing carbon content. The steels containing C max � 0.055% feature a ferriticaustenitic
structure. In the microstructure of solution heat-treated steel with increased
carbon content a carbide eutectic, non-dissolved during the heat treatment, is observed.
Isothermal holding at 480�C results in spinodal decomposition of ferrite with creation of
� and �� phases as well as precipitation in the ferrite of �-Cu phases.
2. Duplex cast steel allows obtaining very high impact energy after the solution heat
treatment, reaching 160 J, however small fraction of eutectic carbides in the cast steel
containing 0.06% C reduces the impact strength to about 118 J. Once the carbide eutectic
creates a network (in the steel containing 0.12% C) the impact strength does not exceed
10 J.
3. Ageing after the solution heat treatment results in approx. 20% increase in
hardness related to precipitation processes in the ferrite, simultaneous with a few-times
decrease in impact energy.
4. Fractographic examinations have shown that fractures of specimens of cast steel
with low carbon content are typical ductile transcrystalline micromechanism. The size of
ductile fracture ‘dimples’ depends clearly on the size of their initiators, which are pretty
large inclusions of third-type sulphides and much smaller precipitates of carbides or
carbonitrides. An increase in carbon content in the cast steel is accompanied by a decline
in ductility areas and fracture surfaces of specimens are of mixed nature, ductile and
brittle.
1. R. A. Perren, T. A. Suter, C. Solenthaler, et al., “Corrosion resistance of super duplex stainless
steels in chloride ion containing environments: investigations by means of a new
microelectrochemical method. II. Influence of precipitates,” Corros. Sci., 43, 727–745 (2001).
2. C. J. Park, V. R. Shankar, and H. S. Kwon, “Effect of sigma phase on the initiation and
propagation of pitting corrosion of duplex stainless steel,” Corrosion, 61, No. 1, 76–83
(2005).
3. J. Tissier, D. Balloy, J. Dairon, et al., “Décarborution sous vide: une solution á la portée des
PME de fonderie,” Fonderie: Fondeur d’Aujourd’hui, No. 246, 28–39 (2005).
4. W. Hubner and E. Leitel, “Peculiarities of erosion-corrosion processes,” Tribology Int., 29,
No. 3, 199–206 (1996).
5. Z. Stradomski, S. Stachura, and D. Dyja, “Technological problems in elaboration of massive
casting from duplex cast steel,” in: Stainless Steel World Conference&Expo, Maastricht,
Netherlands (2005), pp. 363–368.
6. Z. Stradomski and D. Dyja, “Influence of carbon content on the segregation processes in
duplex cast steel,” Arch. Foundry Eng., 7, Issue 1, 139–142 (2007).
7. J. Peultier, F. Barrau, and J. P. Audouard, “Corrosion resistance of duplex and superduplex
stainless steels for air pollution control process systems,” Stainless Steel World, 17, 45–55
(2005).
8. K. A. Bakken, “Cost effective materials selections – what is true?,” in: Stainless Steel World
Conference&Expo, Maastricht, Netherlands (2005), pp. 18–23.
9. D. Dyja and Z. Stradomski, “Quench ageing behavior of duplex cast steel with nano-scale
�-Cu particles,” J. Achiev. Mater. Manufact. Eng., 20, Issue 1-2, 435–438 (2007).
Received 28. 06. 2007
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UDC 539. 4
Influence of Carbides Morphology on Fracture Toughness of Cast Steel
G200CrMoNi4-3-3
Z. Stradomski, 1,a A. Pirek, 1,b and D. Dyja 1,c
1 Czestochowa University of Technology, Institute of Materials Engineering, Czestochowa, Poland
a zbigniew@mim.pcz.czest.pl, b pireka@mim.pcz.czest.pl, c dyjad@mim.pcz.czest.pl
We analyze the influence of small modification of chemical composition of G200CrMoNi4-3-3 cast
steel on the morphology of carbides and on material crack resistance. Using the Termo-Calc
software the volume fraction of carbide phase was determined and the results correlated with
microstructure observations. Crack resistance of cast steel was determined using SENB specimens
and finding critical values of stress intensity factor K Q . Metallographic and fractographic
observations of fracture surfaces allowed identifying the mechanism of cracking.
Keywords: fracture toughness, hardness, carbides, rolls.
Introduction. A specific and separate group of tool materials is represented by steels
and cast steels for mill rolls. Hypereutectoid steels are largely represented in this group, in
which the abrasion resistance is guaranteed by large carbide precipitates according to the
following Zum Gahr equation [1]:
32 /
W d VV � ,
�
where d is size of carbides, V V is volume fracture, � is mean free path, and W is wear
resistance.
Substantial initial diameters of rolls as well as the need of machining related to the
surface wear or changes in the pass geometry make that the heat treatment of those cast
steels is very limited. It is reduced most often to normalizing and stress-relief annealing.
However, not too hard pearlitic matrix under conditions of dry friction shows very good
resistance to abrasive wear, what is indicated by literature data [1–3] and own authors’
research [4, 5].
Cast steels containing substantial amounts of carbon have a drawback consisting in the
presence of large carbide precipitates, which create more or less continuous network of
ledeburite and hypereutectoid cementite. Such microstructure, though favorable from the
point of view of tribological properties, strongly reduces the material crack resistance [3, 6].
Taking into consideration the above aspects of microstructure, we have used
parameters of fracture mechanics to optimize the structure of G200CrMoNi4-3-3 cast
steel. The paper has been focused on determination of the influence of small modification
of chemical composition of G200CrMoNi4-3-3 cast steel on the morphology of carbides
and the material crack resistance.
Materials and Methodology. High-carbon low-alloy cast steel has been used in the
investigation, in which diversified carbides content was obtained through small modification
of chemical composition resulting, however, in substantial increased in volume fraction of
carbide phase. The material for studies was taken from upper neck of mill rolls weighing
around 10000 kg. The chemical composition (in mass %) of studied G200CrMoNi4-3-3
cast steels was specified in Table 1.
Residual stresses and the character of microstructure were analyzed after the as-cast
rolls have been subjected to long-term heat treatment (about 160 h) consisting of
normalizing and tempering at a temperature below A C1 . Based on the chemical composition
© Z. STRADOMSKI, A. PIREK, D. DYJA, 2008
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(1)

Z. Stradomski, A. Pirek, and D. Dyja
of examined heats the transformation temperatures of eutectic ( E �,
C �)
and eutectoid ( S �)
transformation have been determined using the Termo-Calc computer software. Volume
fractions of primary carbides VV ledeburite and of hypereutectoid cementite VV Fe3C have
been determined, taking into account also the normalizing temperature (point in ACm line).
Table 1
Chemical Composition of the Cast Steels
Rolls C Mn Si P S Cr Ni Mo Cu
1 1.89 0.58 0.42 0.028 0.007 1.15 0.58 0.37 0.09
2 2.10 0.54 0.58 0.038 0.010 1.59 0.48 0.52 0.11
3 2.12 0.72 0.55 0.017 0.005 1.13 0.74 0.38 0.12
4 2.16 0.67 0.56 0.025 0.016 1.07 0.62 0.39 0.14
5 2.20 0.59 0.53 0.019 0.006 1.11 0.65 0.40 0.11
6 2.22 0.74 0.61 0.026 0.010 1.06 0.64 0.37 0.12
Results. The influence of carbide-forming elements on the position of transformation
temperatures and carbides volume fractions is specified in Table 2. The obtained results
have been confirmed by microstructural analysis of selected rolls. Some of micrographs
are presented in Fig. 1.
Table 2
The Influence of Carbide-Forming Elements on the Position of Transformation
Temperatures of Fe–Fe3C System and Carbides Volume Fractions
Rolls Chemical
compositions
Point of Fe–C VV VV �VV
C Cr Mo E� C� S� ledeburite Fe3C ledeburite + Fe3C
% % C % %
1 1.89 1.15 0.37 2.021 4.3745 1.38 0 10.90 10.9
2 2.10 1.43 0.52 2.006 4.3725 1.34 4.14 16.63 20.8
3 2.12 1.13 0.38 2.020 4.3750 1.34 4.43 17.14 21.6
4 2.16 1.07 0.39 2.019 4.3749 1.34 6.36 18.18 24.5
5 2.20 1.11 0.40 2.018 4.3746 1.34 8.36 19.24 27.6
6 2.22 1.06 0.37 2.021 4.3752 1.34 9.23 19.78 29.0
Fig. 1. Microstructure of the G200CrMoNi4-6-3 cast steel.
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Influence of Carbides Morphology on Fracture Toughness ...
Precipitations of transformed ledeburite in the cast steel of heat 1, shown in Fig. 1a,
in which according to Table 2 the eutectic reaction should not occur, result from
segregation processes ensued by solidification of massive castings.
The fraction of cementite eutectic, lowered by precipitations of hypereutectoid
cementite, increases from the value of 11 to 29% in cast steel 5 containing 2.22% C
1.06% Cr, and 0.37% Mo (Fig. 1). Very small changes in carbide-forming elements
contents have a significant influence on carbides amount and morphology. As compared
to the as-cast state, the normalizing causes dissolution of part of thick network of
hypereutectoid cementite, also in a Widmannstatten microstructure.
Hardness was measured by the Brinell method according to the PN-EN ISO
6506-1:2002 standard under a load of 7355 N with a steel ball of a diameter of 5 mm. The
results are specified in Fig. 2.
With increasing volume fraction of carbide phase (ledeburite and hypereutectoid
cementite precipitated in the form of more or less continuous network) the propensity for
brittle fracture propagation increases in the structure. The crack resistance of cast steel
with diversified content of carbide phase was evaluated based on the stress intensity factor
K Q , determined in accordance with ASTM E399-90 recommendations. SENB specimens,
with dimensions 80�10�20 mm and mechanically cut 10 mm depth notch, were tested by
three-point bending. Results of tests carried out on an MTS-810 testing machine are
presented in Fig. 3.
Fig. 2 Fig. 3
Fig. 2. Influence of the carbon content on the hardness.
Fig. 3. Influence of the chemical composition on the fracture toughness.
Fig. 4 Fig. 5
Fig. 4. Microstructure of the cast steel below notch in SENB specimens.
Fig. 5. SEM microphotographs of the cast steel.
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Z. Stradomski, A. Pirek, and D. Dyja
Approximately 200% growth in the carbide phase amount, precipitated mainly at
primary boundaries of austenite grains, is accompanied by around 25% decrease in K Q
value. Strong decline in K Q of roll 2 results from substantial amount of phosphorus
precipitated in the form of brittle phosphorus eutectic, revealed both by microscopic and
fractographic examinations.
The mechanism of cracking was analyzed using a scanning and optical microscope
on metallographic microsections taken from regions below the specimens notch root. The
results of observations show that the fracture proceeds along the network of transformed
ledeburite and precipitations of hypereutectoid cementite (Fig. 4), while it goes through
the pearlitic matrix only in short sections.
Fractographic examinations (Fig. 5) confirm observations of the material microstructure.
The material is cracking both along grain boundaries ‘decorated’ with carbides,
what is frequently accompanied by brittle fracture, as well as through pearlite grains,
cracking in a ductile mode. Ductile mechanism of pearlite cracking is caused mainly by
fine globular precipitations of secondary carbides.
Conclusions
1. Increase in carbon content from 1.89% to 2.22% caused a two-times increase in
the volume fraction of ledeburite and hypereutectoid cementite, precipitated in the form of
more or less continuous network.
2. Two-times increase in the content of carbide phase precipitated in the form of
network resulted in around 20% increase in hardness, parallel to crack resistance
decreased by 25%.
3. Low value of stress intensity factor K Q for heat 2 resulted from the presence of
phosphorus eutectic in the alloy misrostructure.
4. The higher than recommended phosphorus content, in particular in high-carbon
cast steels, results in substantial increase in their brittleness and may cause a premature
damage to the roll.
1. K. H. Zum Gahr, “Microstructure and wear of materials,” in: Tribology, Series 10, Elsevier,
Amsterdam (1987), pp. 227–252.
2. Y. S. Liao and R. H. Shiue, “Effect of carbide orientation on abrasion of high Cr white cast
iron,” Wear, 193, 16–24 (1996).
3. You Wang, Tingquan Lei, and Jiajun Liu, “Tribo-metallographic behavior of high carbon
steels in sliding,” Wear, 231, 1–11 (1999).
4. Z. Stradomski and S. Stachura, “Role of microstructure in the mechanism of abrasive wear of
high-carbon steel,” Acta Metall. Slovaca, R. 8, No. 2/2, 388–393 (2002).
5. Z. Stradomski, S. Stachura, A. Pirek, and P. Chmielowiec, “The affect of the amout of
primary carbides on the wear resistance of the G200CrMoNi4-6-3 (L200 HNM) cast steel,”
Inzynieria Materialowa, No. 3, XX–XXIII (2004).
6. S. C. Lim, M. F. Ashby, and J. H. Brunton, “Wear-rate transitions and their relationship to
wear mechanisms,” Acta Metall., 35, No. 6, 1343–1348 (1991).
Received 28. 06. 2007
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UDC 539. 4
Corrosion Fatigue Behavior of Extruded AZ80, AZ61, and AM60 Magnesium
Alloys in Distilled Water
Y. Uematsu, 1,a K. Tokaji, 1,b and T. Ohashi 2
1 Gifu University, Gifu, Japan
2 Brother Industries Ltd, Nagoya, Japan
a yuematsu@gifu-u.ac.jp, b tokaji@gifu-u.ac.jp
Rotary bending fatigue tests were conducted in laboratory air and distilled water using three
extruded magnesium (Mg) alloys AZ80, AZ61, and AM60 with different chemical compositions. In
laboratory air, the fatigue strengths at high stress levels were similar in all alloys because cracks
initiated at Al-Mn intermetallic compounds, whereas AZ80 with the largest Al content exhibited the
highest fatigue strength at low stress levels, which was attributed to the crack initiation due to
cyclic slip deformation in the matrix microstructure. In distilled water, fatigue strengths were
considerably decreased due to the formation of corrosion pits in all alloys, and the difference of
fatigue strength at low stress levels among the alloys disappeared, indicating that the addition of Al
that improved the fatigue strength in laboratory air was detrimental to corrosion fatigue.
Keywords: fatigue, corrosion fatigue, magnesium alloy, crack initiation.
Introduction. Mg alloys have recently received considerable attention due to their
excellent properties such as light weight, high specific strength and stiffness, etc. Wrought
Mg alloys have superior mechanical properties to cast Mg alloys, but various fatigue
properties should be evaluated in detail for their applications to load-bearing components
[1]. Furthermore, it is well known that Mg alloys have poor corrosion resistance [2].
Therefore, understanding the corrosion fatigue behavior of Mg alloys is also very
important [3]. In the present study, rotary bending fatigue tests have been performed in
laboratory air and distilled water using three extruded Mg alloys AZ80, AZ61, and AM60
with different chemical compositions, where the Al and Zn contents are considerably
different. The effect of chemical composition of Mg alloys on corrosion fatigue behavior
was discussed.
Experimental Details. Materials and Specimen. The materials used are extruded
AZ80, AZ61, and AM60 alloys. Their chemical compositions (wt.%) and mechanical
properties are listed in Tables 1 and 2, respectively. The tensile strength increases with
increasing the Al content. The average grain sizes are 12, 17.9, and 8.7 �m for AZ80,
AZ61, and AM60, respectively. Smooth fatigue specimens with a diameter of 8 mm and a
gauge length of 10 mm were machined from the extruded materials. All specimens were
sampled from the same lot extruded bars in order to avoid large scatter in S�N data.
Procedures. Fatigue tests were performed using a 98 Nm capacity rotary bending
fatigue testing machine operating at a frequency of 20 Hz in laboratory air. Corrosion
fatigue tests were conducted using the same testing machine where distilled water was
dropped onto the centre of gauge length by a metering pump whose flow rate was 140
ml/min.
Results and Discussion. Fatigue Behavior in Laboratory Air. Fatigue Strength. In
the following Figures 1, 5 and 6, the test results in laboratory air and distilled water are
shown by open and solid symbols, respectively. The S�N diagram is revealed in Fig. 1.
The fatigue strengths at high stress levels are similar in all alloys, indicating that chemical
composition has little effect. However, the fatigue limits defined as the fatigue strengths at
N � 10 7 cycles are 80 MPa for AZ61 and AM60 and 100 MPa for AZ80. Therefore, the
addition of Al can improve not only tensile strength but also fatigue limit.
© Y. UEMATSU, K. TOKAJI, T. OHASHI, 2008
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Y. Uematsu, K. Tokaji, and T. Ohashi
Table 1
Chemical Compositions of Materials (wt.%)
Material Al Zn Mn Ni Cu Fe Si Pb Ca Sn Mg
AZ80 8.3 0.60 0.23 0.0010 0.0020 0.002 0.030 – – – Bal.
AZ61 6.4 0.74 0.35 0.0012 0.0029 0.001 0.015 0.001 0.001

Corrosion Fatigue Behavior of Extruded ...
AM60, AZ61, and AZ80, revealing that the addition of Al can improve small crack
growth resistance.
It is believed that crack initiation from inclusion at high stress levels results in the
similar fatigue strength regardless of chemical composition, while when low stresses were
applied, cracks initiated due to cyclic slip deformation. Therefore, AZ80 with the highest
Al content and tensile strength has the highest fatigue limit.
Fig. 3. SEM micrographs showing crack initiation site in laboratory air (��150 MPa): (a) AZ80,
(b) AZ61, (c) AM60.
Fig. 4. SEM micrographs showing crack initiation site in laboratory air (��110 MPa): (a) AZ80,
(b) AZ61, (c) AM60.
Fig. 5 Fig. 6
Fig. 5. Relationship between surface crack length and cycle ratio.
Fig. 6. Relationship between crack growth rate and maximum stress intensity factor.
Fatigue Behavior in Distilled Water. Fatigue Strength. The fatigue strengths at high
stress levels in distilled water are similar to those in laboratory air, while fatigue fracture
occurs even if stress levels are lower than the fatigue limit in laboratory air. The fatigue
strengths of all alloys are nearly the same, thus AZ80 that exhibited the highest fatigue
limit in laboratory air is most sensitive to the corrosive environment.
Crack Initiation Behavior. Figure 7 shows SEM micrographs of fracture surface near
crack initiation site at a stress level of 50 MPa that is lower than the fatigue limit in
laboratory air. The specimen was tilted about an angle of 45� in order to observe the
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Y. Uematsu, K. Tokaji, and T. Ohashi
specimen surface. It is clear that the specimen surface is covered by cracked corrosion
product, and corrosion pit shown by allow is recognized at the crack initiation site. Figure 8
represents the specimen surfaces of AM60 tested at a stress level of 50 MPa in distilled
water. In all alloys, the specimen surfaces are covered by corrosion product and many
corrosion pits are formed as typically seen in Fig. 8. However, corrosion pits were not
recognized on the specimen surface or the crack initiation site when higher stresses were
applied, namely test period was short. Therefore, it can be concluded that corrosion pit is
formed at low stress levels, where test period was long, and cracks initiate from the
corrosion pit, leading to the fatigue failure below the fatigue limit in laboratory air.
Fig. 7. SEM micrographs showing crack initiation site in distilled water (��50 MPa): (a) AZ80,
(b) AZ61, (c) AM60.
Fig. 8. Specimen surfaces of AM60 (��50 MPa).
Small Crack Growth Behavior. The relationship between 2c and N N f in Fig. 5
reveals that cracks initiated at the stage where N N f was larger than 0.4 in distilled
water, while at an early stage in laboratory air. It implies that corrosion pits are formed in
an early stage of fatigue life in distilled water. Crack growth rates are shown in Fig. 6 as a
function of K max . The crack growth rates in distilled water are nearly the same as those
in laboratory air, and the dependence of crack growth rate on chemical composition
observed in laboratory air disappears in distilled water.
Fig. 9. Anode polarization curves in distilled water.
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Corrosion Fatigue Behavior of Extruded ...
Effect of Chemical Composition. Figure 9 indicates the anode polarization curves in
distilled water. The corrosion potentials are almost the same in all alloys, while the
corrosion rate is fastest in AZ80. It is believed that the highest sensitivity of AZ80 to
corrosive environment is attributed to the electrochemical nature of AZ80. Therefore, it
can be concluded that the addition of Al can contribute to improving the fatigue limit in
laboratory air, while enhances the sensitivity against corrosive environment. Fatigue
behavior in laboratory air and distilled water was similar between AZ61 and AM60, thus
the addition of Zn has no effect on fatigue strength and corrosion resistance.
Conclusions. Rotary bending fatigue tests were conducted in laboratory air and
distilled water using three extruded Mg alloys AZ80, AZ61, and AM60 with different
chemical compositions. In laboratory air, AZ80 with the largest Al content had the highest
fatigue limit, because crack initiation was due to cyclic slip deformation at low stress
levels. However, corrosion fatigue strengths were almost the same in all alloys, indicating
that the sensitivity against corrosive environment was enhanced by the addition of Al.
1. Y. Uematsu, K. Tokaji, M. Kamakura, et al., Mater. Sci. Eng., A434, 131 (2006).
2. R. S. Stameppa, R. P. M. Procter, and V. Ashworth, Corrosion Science, 24, 325 (1984).
3. Y. Unigovski, A. Eliezer, E. Abramov, et al., Mater. Sci. Eng., A360, 132 (2003).
Received 28. 06. 2007
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UDC 539. 4
Fracture Toughness of Multilayer Pipes
E. Nezbedová, 1,a L. Fiedler, 2,b Z. Majer, 2,3,c B. Vlach, 2,d and Z. Knésl 3,e
1
Faculty of Chemistry, Institute of Materials Science, Brno University of Technology, Brno, Czech
Republic
2
Faculty of Mechanical Engineering, Brno Technical University, Brno, Czech Republic
3
Institute of Physics of Materials, Academy of Science of the Czech Republic, Brno, Czech Republic
a nezbedova@fch.vutbr.cz, b fidlub@post.cz, c majer@ipm.cz, d vlach@fme.vutbr.cz,
e knesl@ipm.cz
Multilayer pipes composed of various materials improve partially the properties of a pipe system
and are frequently used in service. To estimate the lifetime of these pipes the basic fracture
parameters have to be measured. In the contribution a new approach to this estimation is presented.
Special type of a C-shaped inhomogeneous fracture mechanics specimen machined directly from a
pipe has been proposed, numerically analyzed and tested. The corresponding K values are
calculated by FEM and fracture toughness values of HDPE pipes material are obtained.
Keywords: polyethylene pipes, fracture toughness, K-calibration.
Introduction. Polyethylene (HDPE) and polypropylene (PP) materials can be
considered modern and ecologic; they substitute for conventional pipe materials (steel,
cast-iron). This progress is followed by relevant legislation (international standards,
profession directives, national codes, etc.). According to these standards the lifetime of the
newest bimodal type of HDPE [1] is expected to be up to 100 years. This long lifetime is
guaranteed only if tubes are strained with just inner overpressure. Unfortunately, there are
other factors in service, which can reduce this lifetime [2, 3]. These extraordinary
circumstances can evoke creation of the stress raisers that can lead to forming of a crack
and then to brittle failure of the whole pipe system. Using the fracture mechanics
approaches [4–6] there have been developed methods and procedures which are able to
evaluate the resistance of both native material and pipes from the view of a slow [7] and
rapid crack growth [8].
The development of new materials has supported novel technologies, which could
not be used so far in laying of new tubes and sanitation [9]. The so-called multilayer pipes
have received a wider acceptance recently in the field of pipes systems. The purpose of
the development was to improve partially the properties profile of pipes from nonchained
polyethylene by combining with other materials. This method has essentially resulted in
two types of pipes: (i) pipes with dimensional addition of a protective surface and (ii)
pipes with a dimensionally integrated protective surface.
In our contribution we have focused on the second type of multilayer pipes and its
lifetime expectation. Specifically, the fracture toughness was chosen as a relevant
parameter for evaluation of a pipe material resistance to a so-called slow crack growth
(SCG). This type of fracture occurs under long-term service conditions and limits the
lifetime. To estimate fracture toughness of the pipe material a special inhomogeneous
C-shaped specimen machined directly from the pipe (Fig. 1a) was proposed and numerically
analyzed. Based on the numerical results the fracture mechanics parameters K Qd were
estimated for two different temperatures.
Experimental. The three-layer commercial plastic pipe Wavin TS (�110 SDR11)
with its outer and inner layers made of an extremely durable PE material (XSC 50) and its
interlayer PE 100 was chosen as experimental material. The thickness of both inner and
outer layers was 2.5 mm and that of the interlayer was 5 mm (Fig. 1b).
© E. NEZBEDOVÁ, L. FIEDLER, Z. MAJER, B. VLACH, Z. KNÉSL, 2008
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Fig. 1. C-shaped specimen and the experimental setup used for the fracture toughness measurements
(a); schematic of the three-layer pipe (b).
The material mechanical characteristics (tensile modulus E and yield stress � y )of
individual layers were determined from standard tensile tests carried out according to
standard CSN EN ISO 527-1. Tensile test specimens were directly cut from the pipe in the
longitudinal direction of the pipe. Tests were carried out on the universal testing machine
Zwick Z020. The load was measured using 2.5 kN dynamometer and deformation was
determined using an extensometer with accuracy class 0.5. The testing conditions were as
follows: initial gauge length 20 mm, temperature 23�C and �60�C, and crosshead speed
1 mm/min. The obtained values of tensile modulus E and yield stress � y are
summarized in Table 1.
Table 1
a b
The Mechanical Characteristics of the Pipe Layers
Temperature,
E, MPa � y , MPa
�C
Inner/outer layer Intermediate layer Inner/outer layer Intermediate layer
xs xs xs xs
23 827/34 1213/28 16/1 20/0
�60 2740/99 3399/91 45/0 48/0
Fracture mechanics characteristics were determined using the two types of
instrumented Charpy impact testers. The first one was a high-energy impact tester PSW
300E/MFL with impact energy 150 J. The second was a low-energy impact tester
Fraktoskop K4J with impact energy 4 J (Fig. 1a). The notches were made by pressing a
fresh razor blade into the specimens.
The test conditions on the both types of impact testers were as follows: test
temperature 23�C and �60�C, impact rate 1 m/s, and span distance 40 mm.
The specimen 10 mm thick was tested on the high-energy impact tester, while the
specimen of 4 mm thickness was tested on the low-energy impact tester. Notches of three
different depths (3.8, 4.6, and 5.6 mm) were made on 4-mm-thick specimens. In the case
of 10-mm-thick specimens the notches were of the same depth – 4.6 mm. In all cases the
crack tips were located in the interlayer PE 100 material. The resulting values of dynamic
fracture toughness K Qd were calculated according to the equation
K
F S
f( a W).
32 /
BW
Qd � max
Fracture Toughness of Multilayer Pipes
Note. Here and in Table 2: x is the mean value and s is a corresponding standard deviation.
Here Fmax is the maximum load, S is the span distance, B and W are the thickness
and width, respectively, a is the notch depth, and f( a W)
is a geometric factor. The
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(1)

E. Nezbedová, L. Fiedler, Z. Majer, et al.
geometric factor is known only for a homogeneous standard three-point bend specimen [9,
10]. The function f( a W)
corresponding to the used C-shaped inhomogeneous three
layers specimen has to be calculated numerically.
Numerical Model. The numerical model corresponds to the experimental setup. The
material data correspond to those given in Table 1. The numerical analyses were carried
out under plane strain conditions by using a finite element method as implemented in the
standard ANSYS 10.0 system. To estimate the corresponding values of stress intensity
factor K I the standard K-CALC procedure implemented in ANSYS has been applied. As
a result, the values of K I were obtained and the corresponding function f( a W)
was
estimated according to Eq. (1), see Fig. 2. The geometric factor corresponding to the
standard three-point bend specimen is added for comparison. Note that the f( a W)
values are practically independent of Poisson’s ratio. Using Eq. (1) and the results
presented in Fig. 2, the values of the dynamic fracture toughness were estimated (Table 2).
Note that according to the ASTM standard the only valid value of K Ic is obtained for
temperature �60�Cand for the specimen thickness B2 � 10 mm.
The values of dynamic fracture toughness for two different specimen thicknesses and
for temperatures 23�C and �60�C, determined using two types of instrumented Charpy
impact testers, are given in Table 2.
Table 2
Resulting Values of Dynamic Fracture Toughness for Two Different Specimen Thicknesses
Thickness, mm B1 � 4
B2 �10
a, mm 3.8 4.6 5.6 4.6
Temperature,
�C
/
KQd , MPa�m 12
xs xs xs xs
23 3.0/0.4 2.0/0.3 1.2/0.1 2.4/0.2
�60 2.4/0.2 1.8/0.3 1.1/0.6 3.5/0.1
Fig. 2. Correction function f( a W)
for a C-type specimen (middle layer): (1) homogeneous
specimen; (2) temperature T ��60�C; (3) temperature T �23�C; (4) standard three-point bend
specimen [9, 10].
Conclusions. We have studied the lifetime expectation of the three-layer commercial
plastic pipe with dimensionally integrated protective surfaces was investigated. The
fracture toughness is chosen as a relevant parameter for evaluation of the pipe material
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Fracture Toughness of Multilayer Pipes
resistance to a slow crack growth. To evaluate fracture toughness values of the interlayer
PE 100 pipe material the following steps have been made:
� the material parameters (tensile modulus E and yield stress � y ) for both inner
and outer layers of the three layers pipe were determined for temperatures 23�C and
�60�C; � a new inhomogeneous C-shaped fracture mechanics specimen machined directly
from the pipe has been used and the corresponding values of the stress intensity factor K
represented by the geometric factor f( a W)
have been calculated by FEM;
� the values of dynamic fracture toughness for two different specimen thicknesses
and for temperatures 23�C and �60�Cwere determined using two types of instrumented
Charpy impact testers
Acknowledgments. The authors gratefully acknowledge the support provided by the Grant
Agency of the Czech Republic (No. 101/05/0227) for this work.
1. E. Nezbedová, A. Zahradnícková, and Z. Salajka, “Brittle failure versus structure of HDPE
pipe grades,” J. Macromol. Sci. – Physics, B40 (384), 507–515 (2001).
2. J. Hessel, “Mindesbendsdauer von erdverlegten Rohen aus Polyethylen ohne Sandeinbettung,”
Sonderdruck aus 3R International; 40 Jahrgang, Heft 4 (2001), SS. 178–184.
3. A. L. Ward, X. Lu, Y. Huang, and N. Brown, Polymer Testing, 11, 309 (1992).
4. M. Fleipner, “Langsames Risswachstum und Zeitstandfestingkeit von Rohren aus Polyethylene,”
Kunststoffe, 77, No. 1, 45–50 (1987).
5. S. J. Ritchie, P. Davis, and P. S. Leevers, “Brittle–tough transition of rapid crack propagation
in polyethylene,” Polymer, 39, 6657–6663 (1998).
6. ISO/CD 16770: Plastics. Determination of Environmental Stress Cracking (ESC) of
Polyethylene (PE), Full Notch Creep Test (FNCT) and ISO/CD 16 241: Notch Tensile Test to
Measure the Resistance to Slow Crack Growth of Polyethylene Materials for Pipe and Fitting
Products (PENT).
7. ISO 13477:1997 Thermoplastics Pipes for the Conveyance of Fluids. Determination of
Resistance to Rapid Crack Propagation (RCP). Small-Scale Steady-State Test (S4 Test).
8. Y. Savidus, “Progresivní postupy pou�ívané pøi výstavbì potrubních vedení z plastu,” 10
roèník mezinárodní konference Plasty v Rozvodech Plynu [in Czech], Sborník referátù, Praha
(2003), str. 233.
9. ISO 13586: Determination of Fracture Toughness (Gc Mechanics (LEFM) Approach.
and Kc ). Linear Elastic Fracture
10. W. Grellmann, S. Seidler, und W. Hesse, MPK-Prozedur: Prüfung von Kunststoffen –
Instrumentierter Kerbschlagbiegeversuch, Merseburg (2005).
Received 28. 06. 2007
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UDC 539. 4
Fatigue Behavior of Dissimilar Friction Stir Welds between Cast and Wrought
Aluminum Alloys
Y. Uematsu, 1,a Y. Tozaki, 2 K. Tokaji, 1,b and M. Nakamura 1
1 Gifu University, Gifu, Japan
2 Gifu Prefectural Research Institute for Machinery and Materials, Seki, Japan
a yuematsu@gifu-u.ac.jp, b tokaji@gifu-u.ac.jp
Cast aluminum alloy, AC4CH-T6, and wrought aluminum alloy, A6061-T6, were joined by means of
friction stir welding (FSW) technique. The effect of microstructure and post heat treatment on
fatigue behavior of the dissimilar joints was investigated. Near the weld centre, Vickers hardness
was lower than in the parent metals and the hardness minima were observed along the trace route
of FSW tool’s shoulder edge. Tensile fracture took place on A6061 side where the hardness was
minimal, resulting in the lower static strength of the dissimilar joints than AC4CH or A6061.
Fatigue fracture occurred on AC4CH side due to casting defects and the fatigue strength of the
dissimilar joints was similar to that of AC4CH, but lower than that of A6061. Friction stir process
(FSP) and post heat treatment successfully improved the fatigue strength of the dissimilar joints up
to that of the parent metal, A6061.
Keywords: fatigue, friction stir welding, dissimilar joint, aluminum alloy.
Introduction. Aluminum alloys are increasingly used for transportation systems,
particularly in automobiles, with the aim of weight saving. Wrought and cast aluminum
alloys are applied to body skin and complex shape components, respectively, and joining
between both alloys is often required. Friction stir welding (FSW) is a recently developed
solid state welding process and now being used for joining aluminum alloys for which
fusion welding is difficult [1, 2]. Furthermore, it is known that FSW technique is suitable
for joining dissimilar metals because of solid state process [3]. In order to apply dissimilar
joints to load-bearing components, it is significant to understand their fatigue behavior. In
the present study, the fatigue behavior of the dissimilar FSW joints between cast
aluminum alloy, AC4CH-T6 and wrought aluminum alloy, A6061-T6, was investigated.
The effect of microstructure and post heat treatment on fatigue behavior is discussed.
Experimental Details. Materials. The materials used are cast aluminum alloy,
AC4CH-T6, and wrought aluminum alloy, A6061-T6. Their chemical compositions
(wt.%) and mechanical properties are listed in Tables 1 and 2, respectively. The
microstructures of the parent metals are shown in Fig. 1. A typical dendrite structure of
cast aluminum alloy is recognized in AC4CH (Fig. 1a), while elongated grains due to
rolling process are seen in A6061 (Fig. 1b), where the average grain size measured along
the rolling direction was about 90 �m.
Welding Condition and Specimen. Plates with a thickness of 5 mm were cut from
casting blocks of AC4CH by wire cut electric spark machining. AC4CH plates were butt
welded with A6061 plates of the same thickness by FSW technique to form the stock from
which fatigue specimens were machined. The upper and lower skins of the stock were
removed by 0.5 mm depth by milling process. The configuration of fatigue specimens is
shown in Fig. 2. The centre of the gauge section corresponds to the welding line and the
loading direction is perpendicular to the welding direction. The friction stir tool was
composed of a pin and a shoulder whose diameter is 6 and 14 mm, respectively. The
tool-to-workpiece angle was 3� from the vertical axis. The plates were joined with the tool
travel speed of 150 mm/min and the tool rotational speed of 1000 rpm. A6061 was
arranged on the advancing side (AS) where the tool travel direction coincides with the
© Y. UEMATSU, Y. TOZAKI, K. TOKAJI, M. NAKAMURA, 2008
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Fatigue Behavior of Dissimilar Friction Stir Welds ...
Table 1
Chemical Compositions of Materials
Material Si Mg Zn Fe Ni Ti Sr Cu Mn Cr
AC4CH-T6 7.10 0.36 0.01 0.12 0.022 0.11 0.005 – – –
A6061-T6 0.58 0.96 0.02 0.41 – 0.04 – 0.28 0.03 0.23
Table 2
Material 0.2% proof stress
�02 . , MPa
AC4CH-T6
A6061-T6
165
275
Mechanical Properties of Materials
Tensile strength
� b , MPa
230
310
Elongation
�, %
5.2
12.0
Fig. 1. Microstructures of parent metals: (a) AC4CH, (b) A6061.
Fig. 2. Configuration of fatigue specimen.
Elastic modulus
E, GPa
72.5
68.3
tool rotational direction. Dissimilar joints, in which A6061 was arranged on the retreating
side (RS), were also examined, but there existed no notable differences in microstructure,
hardness profile and tensile strength.
The fatigue fracture of the as-welded joints took place on AC4CH side due to
casting defects. Therefore, friction stir process (FSP) was applied to as-welded joints in
order to eliminate casting defects in the gauge section. The friction stir tool was inserted
in AC4CH at the locations of 6 and 12 mm away from the weld centre. The tool geometry,
tool travel and rotational speeds in FSP were the same as those in FSW. Furthermore, post
T6-heat treatment was applied to FSPed joints. Hereafter, the specimens are referred to as
as-welded (FSPed) and post heat treated (PHTed) joints.
Procedures. Axial fatigue tests were conduced on an electro-hydraulic fatigue testing
machine at a frequency of 10 Hz and a stress ratio R ��1 (fully reversed loading) in
laboratory air.
Results and Discussion. Microstructure. Figure 3 shows a macroscopic view of the
longitudinal section near the weld zone in an as-welded joint. It can be seen that both
materials are sufficiently stirred in the weld zone, where AC4CH on the RS moves to the
AS near the upper surface, while A6061 on the AS moves to the RS near the lower
surface. The magnified views of the regions A ~ D in Fig. 3 are revealed in Fig. 4. In
AC4CH near the weld centre (Fig. 4a), dendrite structure completely disappears and
eutectic silicon distributes uniformly. In A6061 near the weld centre (Fig. 4c), equiaxed
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Y. Uematsu, Y. Tozaki, K. Tokaji, and M. Nakamura
fine grains, whose average size is about 8 �m, are seen. It is believed that the grain
refinement of A6061 is due to dynamic recrystallization during welding process [1].
Figure 4b shows the region B which is the boundary between AC4CH and A6061. The
boundary line between both materials is distinctly visible, indicating that FSW is a solid
state process. In the region D (Fig. 4d), both materials are arranged in alternative layers
due to stirring under solid state.
Fig. 3. Macroscopic appearance in cross section of as-welded joint.
Fig. 4. Microstructures of as-welded joint: (a), (b), (c) magnified views of region A, B, C, and
(d) region D in Fig. 3, respectively.
Macroscopic appearance in the cross section of an FSPed joint is shown in Fig. 5, in
which the dotted lines represent the locations of the centre of friction stir tool during FSP.
Both materials are stirred more severely in the vicinity of the weld centre of the FSPed
joint. The microstructure of FSPed AC4CH area is similar to that of the region A in Fig. 3
(Fig. 4a). In the PHTed joint, it was found that remarkable grain growth took place near
the weld centre in A6061 [1], whereas there was no or little influence on the microstructure
in AC4CH.
Fig. 5. Macroscopic appearance in cross section of FSPed joint.
Hardness Profile. The Vickers hardness profiles are shown in Fig. 6. The as-welded
joint experiences softening inside the weld zone, which may be attributed to the
dissolution of precipitates due to temperature rise during FSW process. The hardness
minima are located on the both sides about 7 mm away from the weld centre, as shown by
arrow A in Fig. 6. The distance between the hardness minima coincides with the
diameter of FSW tool’s shoulder, indicating that remarkable softening took place along
the trace route of FSW tool’s shoulder edge. Such hardness minima are also recognized in
A6061-T6 FSW joints [1]. The softening area expands to AC4CH side in the FSPed joint.
The hardness minima are observed as shown by arrow B in the figure, which correspond
to the locations of tool’s shoulder edge during FSW and FSP. The PHTed joint exhibits
nearly the same hardness value as the parent metals.
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Fig. 6. Hardness profiles.
Fatigue Behavior of Dissimilar Friction Stir Welds ...
Tensile Strength. The average tensile strength, � b , of three as-welded joints was
198 MPa, which was lower than those of the parent metals. It was found that all joints
fractured on A6061 side where the hardness was minimal.
Fatigue Strength. Figure 7 represents the S�N diagram. The fatigue strength of
the as-welded joint is similar to that of the parent metal, AC4CH. It should be noted that
the fatigue fracture took place on AC4CH side and the location of fracture was different
from tensile fracture. SEM micrograph of fracture surface near crack initiation site of an
as-welded joint is revealed in Fig. 8a. Casting defect is recognized at the crack initiation
site, thus resulting in the similar fatigue strength to the parent metal, AC4CH. On the
other hand, the FSPed joint shows nearly the same fatigue strength as the parent metal,
AC4CH, in high stress region, but considerably higher fatigue limit. Figure 8b represents
SEM micrograph of fracture surface near crack initiation site of an FSPed joint, where
casting defect is not seen. This indicates that casting defects were eliminated by FSP,
which led to the improvement of fatigue limit. Fatigue fracture of the FSPed joints took
place at the locations of the hardness minima, arrow B in Fig. 6. It is believed, therefore,
the fatigue strength in high stress region was not improved due to the softening in the
weld zone. The fatigue strength of the PHTed joint is nearly the same as that of the parent
metal, A6061, due to the recovery of hardness by post heat treatment. However, fatigue
fracture still occurred along the trace route of FSW tool’s shoulder edges shown by arrow
B in Fig. 6.
Fig. 7. S �N diagram.
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Y. Uematsu, Y. Tozaki, K. Tokaji, and M. Nakamura
Fig. 8. SEM micrographs showing crack initiation site: (a) as-welded (��160 MPa), (b) FSPed
(��160 MPa).
Conclusions. Fully reversed axial fatigue tests were conducted using friction stir
welded dissimilar joints between cast aluminum alloy, AC4CH-T6, and wrought aluminum
alloy, A6061-T6. The dissimilar joints showed nearly the same fatigue strength as the
parent metal, AC4CH, because cracks were initiated from casting defects. By the
application of both friction stir process and post heat treatment, the fatigue strength of
dissimilar joints was successfully improved up to that of the parent metal, A6061.
1. Y. Uematsu, K. Tokaji, Y. Tozaki, and H. Shibata, Proc. of the 16th European Conference of
Fracture (ECF 16) (2006).
2. M. A. Sutton, B. Yang, A. P. Reynolds, and T. Taylor, Mater. Sci. Eng., A323, 160 (2002).
3. A. Steuwer, M. J. Peel, and P. J. Withers, Mater. Sci. Eng., A441, 187 (2006).
Received 28. 06. 2007
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UDC 539. 4
Mechanical Properties and Fracture Behavior of High-Strength Steels
R. Mušálek, 1,a P. Haušild, 1,b J. Siegl, 1,c J. Bensch, 1,d and J. Sláma 2,e
1
Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of
Materials, Prague, Czech Republic
2 TKZ, ŠKODA AUTO a.s., Mlada Boleslav, Czech Republic
a radek.musalek@fjfi.cvut.cz, b hausild@fjfi.cvut.cz, c jan.siegl@fjfi.cvut.cz,
d jan.bensch@fjfi.cvut.cz, e jan.slama@skoda-auto.cz
Typical thicknesses of high-strength steels (HSS) sheets used in the car industry are inapplicable for
standardized testing procedures. The aim of this study is to propose an appropriate methodology for
testing and comparing of thin HSS sheets. Microstructures were observed by means of light and
scanning electron microscopy. The modified Charpy impact tests and fracture toughness tests were
used in order to compare the fracture properties of three different HSS sheets (Docol 1200 M,
Multiphase 1200 and BTR 165). Ductile-to-brittle transition curves and tearing resistance (J�� a)
curves were measured. From the fracture toughness linked to the specimen thicknesses the value of
fracture toughness KIc was estimated. Fractographic analysis of broken specimens has revealed
that due to the fine microstructure of mixed ferrite-martensite fracture mechanism remains ductile
even at low temperatures (down to �100�C). Keywords: fracture toughness, Charpy impact energy, fractography, high-strength steel.
Introduction. High-strength steels are widely used in automobile industry for the
reinforcement parts, e.g., door or b-pillar reinforcement. Their high strength makes it
possible to use smaller cross sections, which leads to the reduction of car weight and, thus,
of fuel consumption. Dues to extensive plastic deformation, high-strength steel parts are
also able to absorb high impact energy during a crash, which improves car crew safety.
Therefore the mechanical properties of these materials are of critical importance. So far,
the standardized tests for the HSS sheets have not been designed. We propose a
methodology for testing of thin HSS sheets by means of fracture mechanics and
fractographic analysis.
Materials and Methods. Metallographic observation using light microscope
(Neophot 32) and scanning electron microscope (JEOL JSM 5510LV) revealed fine
ferritic-martensitic microstructures shown in Fig. 1. According to the observed microstructures
and available tensile tests, it is concluded that due to thermomechanical
treatment during the manufacturing process, rolling has relatively small influence on the
isotropy of the observed materials.
The modified Charpy specimens for the impact toughness test [1] and the CT
specimens for the fracture toughness test [2] were prepared from three high-strength steel
sheets using a waterjet (for steel Docol 1200 M) and laser (Multiphase 1200 and BTR
165). All specimen dimensions corresponded to the standard [1, 2] except for the
specimen thickness, which was equal to that of available steel sheets (Table 1).
The impact energy required to break the modified V-notched Charpy impact
specimens into two pieces was measured using Charpy impact equipment with the
maximum energy 150 J. The specimens were cooled in the liquid nitrogen or mixture of
liquid nitrogen and ethanol. The test temperature was measured by a thermocouple. The
time interval between cooling and testing of the specimen was less than 5 seconds (usually
2 or 3 seconds).
Fracture toughness tests were conducted on CT specimens at room temperature
using the Inova ZUZ 50 hydraulic loading machine. The testing procedure followed the
©R.MUŠÁLEK, P. HAUŠILD, J. SIEGL, J. BENSCH, J. SLÁMA, 2008
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R. Mušálek, P. Haušild, J. Siegl, et al.
ASTM 1820-99 [2] standard: a sharp fatigue crack was prepared, then the dependency of
applied load vs. displacement was measured and the crack growth was studied using the
light microscope.
Fractographic analysis using scanning electron microscope JEOL JSM-840A was
carried out on the fracture surfaces of broken specimens.
Table 1
Chemical Composition of Tested High-Strength Steels (wt.%)
Material C Si Mn P S Cr Mo Al Ti B Nb
Docol
1200 M
0.12 0.20 1.60 0.015 0.002 – – �0.03 – – 0.015
Multiphase
1200
0.13 0.12 1.30 �0.020 �0.002 0.25 – 0.03 0.05 – –
BTR 165 0.19–
0.25
a
0.15–
0.50
1.10–
1.40
�0.025 �0.015 �0.35 �0.35 0.02–
0.06
b
0.02–
0.05
0.002–
0.005
Fig. 1. Microstructure of tested steels: (a) Docol 1200 M, (b) Multiphase 1200, and (c) BTR 165.
Experimental Results and Discussion. The modified Charpy impact test has
revealed ductile-to-brittle transition behavior of the high-strength steel sheets shown in
Fig. 2. Ductile-to-brittle transition temperature was determined to be lower than �100�C. Due to the different thicknesses of tested sheets, the impact energy value was normalized
by the specimen thickness to the impact toughness KCV. The highest value of the impact
toughness above the transition temperature was observed for Docol 1200 M steel.
Fracture toughness K c of the observed materials was determined (Table 2). Due to
the small thicknesses B of the tested materials, the plane strain condition was not
satisfied, and the fracture toughness value had to be linked to the specimen thickness.
However, the value of fracture toughness under plane strain condition K Ic
can be
estimated from formula [4]:
� K �
c
Kc �K c � � I �
I 1 �
B �R
�
p �
14
4
.
.
(1)
2
02 .
The load vs. displacement curve and known crack lengths can be used to evaluate
the tearing resistance curves (J�� a)
(see Fig. 3) according to the formula:
2A
J �
Bw ( � a)
, (2)
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c
–

Mechanical Properties and Fracture Behavior ...
where A is the area under the load vs. displacement curve, B is the specimen thickness,
w is specimen width, and a is crack length.
These curves give some idea about the resistance of the material against ductile
tearing. The steeper curve corresponds to the higher resistance. From these curves it can
be observed that Docol 1200 M and Multiphase 1200 have a very similar tearing
resistance. Lower resistance of the BTR 165 steel can be due to the smaller thickness of
this sheet and the higher influence of shear mode III on crack propagation.
Table 2
Material B,
mm
Docol 1200 M 2.0
2.0
Multiphase 1200 2.0
2.0
2.0
BTR 165 1.5
1.5
1.5
Measured Values of Fracture Toughness
Rp02 . ,
MPa
1061
1061
1148
1148
1148
1243
1243
1243
Kc ,
MPa�m 12 /
107.95
115.34
136.04
122.51
119.05
119.22
126.31
106.01
KI c ,
� 12 /
MPa m
(estimate)
56.00
57.51
64.39
61.77
61.06
58.79
60.14
56.06
Fig. 2. Ductile-to-brittle transition curves. Fig. 3. Tearing resistance curves.
Fractographic analysis of broken Charpy specimens has confirmed that failure
mechanisms of tested HSS sheets remain ductile even at a low temperature (down to
�100�C). Due to the small thickness, shear lips were observed on fracture surfaces of all
specimens tested above the transition temperature. Ductile dimples were observed on the
whole fracture surface of specimens broken above the transition temperature. Below the
transition temperature mostly features of cleavage fracture were observed (Fig. 4).
Fractographic analysis of broken CT specimens has shown that the crack was
initiated at the tip of the fatigue pre-crack. In the first stage crack propagated in the mode I,
and then, the crack propagated in the mixed mode I+III due to the small thickness and
shear stress present in the material.
Ductile dimples stretched in the direction of crack growth were observed on some
fracture surfaces of the specimens broken above the transition temperature (Fig. 5).
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R. Mušálek, P. Haušild, J. Siegl, et al.
Fig. 4 Fig. 5
Fig. 4. Typical morphology of Charpy specimen fracture surface broken below the transition
temperature. (Docol 1200 M, test temperature ��190�C.) Fig. 5. Typical morphology of Charpy specimen fracture surface broken above the transition
temperature. (Docol 1200 M, test temperature �20�C.) Conclusions. With respect to the slight differences in the specimen thickness of
different materials, it has been found that from the point of view of fracture mechanics all
the three observed high-strength steels have very similar mechanical properties.
The ductile-to-brittle transition temperature is beyond the typical high-strength steel
application range The observed HSS sheets remained ductile even at a rather low
temperature, which was proven by the fractographic analysis.
It has been confirmed that a new approach to the thin HSS sheets testing by the
means of fracture mechanics is applicable and provides new information on the behavior
of high-strength steel materials under the dynamic loading. The designed method is used
for further material testing of HSS sheets.
Acknowledgments. The authors acknowledge the support from the ŠKODA AUTO, a.s.
company. This project was supported by the Ministry of Education, Youth, and Sport of the Czech
Republic in the frame of the project MSM 6840770021.
1. ÈSN EN 10 045-1. Charpy Impact Test [in Czech], Èeský Normalizaèní Institut (1998).
2. ASTM Standard E 1820-99. Standard Test Method for Measurement of Fracture Toughness,
Annual Book of ASTM Standards (1999), pp. 972–1005.
3. Y. J. Chao, Jr., J. D. Ward, and R. G. Sands, “Charpy impact energy, fracture toughness, and
ductile-brittle transition temperature of dual phase 590 steel,” Mater. Design, 28, 551–557
(2007).
4. G. R. Irwin, “Fracture transition for a crack traversing a plate,” J. Basic Eng., 82, 417–425
(1960).
5. R. Mušálek, Special Materials Characteristic of High-Strength Sheet for Automotive Industry
[in Czech], Master’s Thesis, FNSPE, CTU Prague (2006).
Received 28. 06. 2007
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UDC 539. 4
In Situ Scanning Electron Microscopy Study of Fatigue Crack Propagation
L. Jacobsson, 1,a C. Persson, 1,b and S. Melin 2,c
1 Division of Materials Engineering, Lund University, Lund, Sweden
2 Division of Mechanics, Lund University, Lund, Sweden
a lars.jacobsson@material.lth.se, b christer.persson@material.lth.se, c solveig.melin@mek.lth.se
The fatigue crack propagation rate is influenced by various mechanisms at the very vicinity of the
crack tip, e.g., local plasticity and/or creep, microcracking, crack branching, and crack closure
induced by plasticity and roughness. To study these mechanisms and their influence on crack
propagation rate during different loadings, in situ scanning electron microscope studies have been
performed. Throughout the load cycles images were taken and analyzed with an image analysis
technique to measure the displacements around the crack tip. The obtained data can be used to
determine compliance curves at any point along the crack, crack shapes, and the displacement field in
the crack tip vicinity. The technique has been used to analyze which mechanisms of crack propagation
are realized during, e.g., fatigue with overloads, and thermomechanical fatigue. The results were
compared with results from measurements using the direct current potential drop technique, and it
was found that various load conditions promote different mechanisms for crack propagation.
Keywords: fatigue, crack propagation, scanning electron microscope, crack shape, crack
closure, potential drop.
Introduction. It is of interest to study the material in the crack tip vicinity to
understand the effects of material plasticity around the crack tip, roughness of the crack
faces, microstructure, stresses, and deformations, on the crack propagation. Elber [1, 2]
introduced the concept of crack closure where the maximum stress level at the crack tip is
critical. The maximum load, is calculated from the closure level, where the crack tip is
under zero load, and the applied stress intensity factor range. To measure the crack closure
load level, a number of different measurement techniques are used. Song and Shieh [3]
used the direct current potential drop technique to find the crack closure level, whereas
the ASTM E647-99 [4] recommends to apply the crack mouth opening displacement.
Also, there are different techniques using microscope images to measure the displacements
along the crack.
The aim of this study was to determine the deformations along the crack, and how
the deformations are affected by the different crack propagation mechanisms. High
resolution images from an in-situ scanning electron microscope was used to measure
deformations at the crack tip vicinity, and the potential drop technique was used to
measure the contact between the crack surfaces.
Experimental Setup. The fatigue crack propagation experiments were performed
within a scanning electron microscope (SEM), using a small electrically driven load stage
to perform the load cycles, also described by Andersson et al. [5]. The test specimens had
dimensions of 70�10 mm and were cut from 0.5 mm Inconel 718 foil. The specimens
were prepared with a single-edge-notch tension (SENT) crack, that was pre-cracked in a
servohydraulic load frame to a length of 0.7–1.0 mm. The specimens were etched to
produce a recognizable pattern on the surface of the specimen for the SEM observations.
The specimens were prepared with thin wires welded at the crack mouth to measure the
electrical potential drop signal over the crack. A direct current of 1.0 A was passed
through the specimen and the potential drop signal was amplified before saved in the
computer. The crack propagation rate and the crack closure level were determined. A
summary of the performed experiments is found in Table 1.
© L. JACOBSSON, C. PERSSON, S. MELIN, 2008
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L. Jacobsson, C. Persson, and S. Melin
Table 1
Experimental Conditions for the Four Crack Propagation Experiments
Experiment a, �m �K ,MPa�m 12 /
�Keff ,MPa�m 12 / R ��min �max
i � 740 16.6 3.1 0.01
ii � 945 19.7 10.0 0.01
iii � 1673 43.3 26.3 0.01
iv � 1764 65.0 42.0 0.02
Image Analysis Method. A new image analysis method was developed to measure
displacements in the crack tip vicinity from high resolution SEM images. Images were taken
along the crack throughout the loading cycles. The displacements between different images
were determined using a cross-correlation function that recognized a selected area of one
image in another image, taken at a different load. The area was placed within 2–10 �m
from the crack, where the deformation within the material was negligible. Compliance
curves and crack shapes were determined from the measured displacement field.
Results and Discussion. Crack shapes and compliance curves were determined
during a number of experiments with different loading histories. Compliance curves from
points at different distances from the crack tip are compared in Fig. 1. The compliance
curve measured at the crack mouth showed negligible influence from the plastic zone, and
had a small knee at a higher load than the compliance curves measured at the crack tip,
that showed clear effects from the plastic zone and closure of the crack surfaces. The knee
on the curves from the potential drop (PD) measurements showed in Fig. 2a, indicates the
closure level. Above this level the crack was fully open and the change in electrical
conductivity was only due to the high stresses in front of the crack, and below this level
the contact between the crack surfaces increased with decreasing load. The load level at
the knee on the PD-curves was higher than that at the knee on the compliance curves
measured at the crack mouth.
Fig. 1. Compliance curves measured at three different distances from the crack tip: (�) 2�m;
(�) 20�m; (�) at the crack mouth.
The crack shape obtained by linear elastic fracture mechanics (LEFM) considerations
does not always describe the true crack shape well because of the influence from the
plastic zone and the microstructure. The LEFM solutions, as well as crack shapes
compensated for closure levels from compliance curves and PD measurements, are shown
in Fig. 3. The LEFM solution will be the same, independent of the closure level when the
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a b
In Situ Scanning Electron Microscopy Study ...
Fig. 2. Compliance curve with closure level at 1200 N (a) and the corresponding PD-curve with
12 /
closure level at 1700 N (b) for K max �65 MPa�m , R � 0.02, overload ratio 1.26, a � 1.8 mm,
specimen thickness 0.5 mm, and displacements measured 15 �m from the crack tip. (Experiment iv.)
Fig. 3. Experimental results are compensated for the effective stress intensity factor range measured
from the compliance curve (�) and from the PD signal (�). (Experiment iv. The opening
displacements divided by the effective stress intensity factor range. The solid line shows the LEFM
solution.)
a b
Fig. 4. Crack shapes (a) and �-deformations (b) divided by effective stress intensity factor range
versus distance from crack tip for the four experiments. (Solid line is the LEFM solution.)
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L. Jacobsson, C. Persson, and S. Melin
displacement divided by the effective stress intensity factor range is plotted. When the
experimental results were divided by the closure levels measured from the compliance
curves and the PD-curves, the results diverged (Fig. 3).
In Fig. 4a, the crack shapes are plotted for four different experiments (Table 1). This
close to the crack tip, the microstructure and the change in crack direction affects the
crack shape. In Fig. 4b, the deformation was divided with the effective stress intensity
factor found from compliance curves. The results showed similarities between the four
experiments and also the LEFM solution was close to the experimental results. The crack
tip is shown in Fig. 5.
Fig. 5. SEM image of the crack tip at maximum load. (Experiment iii.)
Conclusions. Experiments have been performed within a SEM and the images were
used to determine deformations in the vicinity of the crack tip. Compliance curves were
determined and compared with results from PD measurements. The PD measurements
gave higher values for the crack closure load than the compliance measurements. When
the experimental results, compensated for crack closure were compared with the LEFM
solution, the crack shapes at the crack tip vicinity became comparable even when the
crack shapes were irregular due to the microstructural variations.
Acknowledgments. The authors give their acknowledgements to the Swedish Gas Turbine
Center for the financial support.
1. W. Elber, Eng. Fract. Mech., 2, 37–45 (1970).
2. W. Elber, in: Damage Tolerance in Aircraft Structures, ASTM STP 486 (1971), pp. 230–242.
3. P. S. Song and Y. L. Shieh, Int. J. Fatigue, 26, 429–436 (2004).
4. Standard Test Method for Measurement of Fatigue Crack Growth Rates, ASTM E647-99
(1995).
5. M. Andersson, C. Persson, and S. Melin, Int. J. Fatigue, 28, 1059–1068 (2006).
Received 28. 06. 2007
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UDC 539. 4
Grain Boundary Influence during Short Fatigue Crack Growth Using a
Discrete Dislocation Technique
P. Hansson 1,a and S. Melin 1,b
1 Division of Mechanics, Lund University, Lund, Sweden
a per.hansson@mek.lth.se, b solveig.melin@mek.lth.se
We have studied the effect of a grain boundary in front of a short edge crack on its propagation
under cyclic loading conditions in bcc iron. The used model is a combination of a discrete
dislocation formulation and a boundary element approach where the boundary is described by
dislocation dipole elements, while the local plasticity is modeled by discrete dislocations. The grain
boundary is considered impenetrable, but dislocations positioned in the vicinity of a grain boundary
give raise to high stresses in neighboring grains which, eventually, results in nucleation of
dislocations and a spread of the plastic zone into the next grain.
Keywords: fatigue, grain boundary, discrete dislocation.
Introduction. It is well known that the behavior of short cracks differs from that of
long cracks due to the relative large plastic zone and strong influence of the surrounding
microstructure. Experimental studies have shown that short cracks grow through a single
shear mechanism [1] and that they can grow at load levels well below the threshold value
for long cracks at high rates. They can therefore not be treated by the standard methods
used for long cracks.
For very low growth rates, in the order of a few Burgers vectors per cycle only, it is
important to account for the discrete dislocations within the material. Authors [2, 3] have
developed such a discrete dislocation model for a long Mode I crack to study the cyclic
crack-tip plasticity and plastically induced crack closure. A similar model has also been
developed in [4] to study the influence of grain boundaries on short mode I cracks.
In this study, a discrete dislocation model, were both the geometry and the plasticity
are described with discrete dislocations, is used to study a short edge crack subjected to
fatigue loading. The plasticity is in this study restricted to two grains, and the change in
growth behavior due to the spread of plasticity between grains is investigated.
Statement of the Problem. The growth of a microstructurally short edge crack
located within one grain, subjected to fatigue loading (Fig. 1), has been investigated under
plane strain and quasi-static conditions. The crack is assumed to grow in a pure shear
mechanism due to nucleation, glide and annihilation of discrete dislocations along slip
planes in the material. The initial crack of length a0 and inclined at angle � to the free
edge normal is located within a semi-infinite body. The load is applied parallel to the free
�
�
edge and is varied between a maximum value, � yy max , and a minimum value, � yy min . In
this study, two neighboring grains are considered, with both grain boundaries parallel to
the free edge. The grain boundaries are considered to be dislocation barriers, which the
dislocations can not pass and will not contribute to the overall stress field. Nucleation and
glide of dislocations is restricted to one slip direction in each grain, inclined at angles �
and � to the free edge normal and with the slip direction in the first grain coinciding with
the initial crack direction.
Initial Conditions. The material in this study is pure iron and is assumed to be linear
elastic. The material parameters at room temperature are shown in Table 1 [5] together
with the geometrical data for the initial edge crack given in Fig. 1.
© P. HANSSON, S. MELIN, 2008
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P. Hansson and S. Melin
Table 1
Material Data for bcc-Iron and Geometrical Data for the Edge Crack
Shear modulus �, GPa 80 Burgers vector b, nm 0.25
Poisson’s ratio � 0.3 Lattice resistance �cr , MPa 40
Fig. 1. Initial geometry of the short edge crack.
Discrete Dislocation Technique. The model used in this study rests solely on a
discrete dislocation formulation, describing both the geometry and the plasticity in the
grains by discrete dislocations. The external boundary, defined as the free edge together
with the crack itself, is modeled using dislocation dipole elements [6]. A dipole element
consists of two glide dislocations and two climb dislocations, with equal size but opposite
direction of the two dislocations of same kind. The dislocations are located at the end
points of the element, while the stresses in the element are calculated at the element center
point.
The stress at an arbitrary point is calculated as the sum of the stress contributions
from the physical dislocations describing the plasticity, the dislocations forming the dipole
elements and the applied external load. The magnitudes of the dipole dislocations are
determined from an equilibrium equation, Eq. (1), describing the normal and shear stress
along the external boundary. Knowing that the normal and shear stresses must equal zero
along the free edge and along the parts of the crack that is open, the magnitudes of the
dipole dislocations can be calculated.
Gbboundary �bGinternal ���0. (1)
In Eq. (1), G is matrix containing influence functions [7], describing the stress field from
a dislocation along the external boundary, b boundary is a vector holding the magnitudes of
the dislocations in the dipole elements, b is the Burgers vector of the material, G internal
is a vector containing the influence functions for the physical dislocations, and � is a
vector containing the contribution from the applied external load along the external
boundary.
Dislocation Nucleation. Nucleation of new dislocations is assumed to occur if the
resolved shear stress at a possible nucleation site exceeds the nucleation stress. Dislocations
nucleate in pairs, consisting of two dislocations of equal size but opposite sign separated
by a small distance r nuc . The definition of a positive and negative dislocations nucleated
at the crack tip is shown in Fig. 2a. It is assumed that nucleation is possible both in front
of the crack tip and at the grain boundary between the two grains.
The nucleation stress is here defined as the lowest stress at the nucleation point for
which the positive dislocation in the newly nucleated dislocation pair travels inwards in
the material immediately after nucleation. This definition results in a geometry dependence
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Grain Boundary Influence during Short Fatigue Crack Growth ...
of the nucleation stress and, therefore, the nucleation stress is not the same in front of the
crack as at the grain boundary. A more thorough discussion on the choice of nucleation
stress is found in [6]. In order to determine when, and on which slip plane the next
nucleation of a dislocation pair will take place, the resolved shear stress is calculated at all
possible nucleation sites for each load level.
a b
Fig. 2. Nucleation condition and definition of positive and negative dislocation at the crack tip (a)
and at the grain boundary (b).
Crack Growth. It is assumed that no dislocations exist within the material prior to the
first load cycle. When the applied load gets sufficiently high, dislocation pairs will
nucleate from the crack tip. A positive dislocation glides inwards in the material
immediately after nucleation along its slip plane as long as the resolved shear stress at its
position exceeds � cr , whereas the negative dislocations will remain at the crack tip. These
dislocations shield the crack tip and the load must therefore be increased before more
dislocations will nucleate. The positive dislocations pile up at the first grain boundary,
resulting in high stresses on the opposite side of the grain boundary. Eventually, these
high stresses will result in nucleation of dislocations in the second grain. Also in this grain
the positive dislocation will move inwards in the material immediately after nucleation
whereas the negative one remains at the grain boundary. This process of dislocation
nucleation in the two grains continues until the maximum load is reached and the load
starts to decrease. Load reversal eventually results in dislocation glide in the opposite
direction, back towards the crack. When a positive dislocation gets sufficiently close to its
negative counterpart, the two dislocations annihilate resulting in crack growth in the
corresponding direction by one b, under the assumption that no healing of the crack
surfaces is allowed. A more detailed description of the crack growth model used can be
found in [6].
Results. In order to investigate the influence of plasticity spread on the crack growth
behavior, the angle � shown Fig. 1 is varied to regulate the resistance to dislocation
nucleation in the second grain, and the results were compared to results obtained by
restricting the plasticity to one grain only. The results of the simulations are presented in
Fig. 3, where Fig. 3a shows the number of dislocations, N, in the two grains for different
applied load levels during the loading phase, and Fig. 3b – during unloading. It can be
seen that when allowing the plasticity to spread into the next grain, the number of
nucleated dislocations in the first grain increases, as compared to the one-grain model. It
can also be seen that a higher number of dislocations are present at the minimum load.
This happens because the negative dislocations in the second grain reduce the stress field
from the piled-up dislocations in the first grain, allowing more dislocations to exist in this
grain. A result of this is, somewhat surprisingly, that the obtained crack growth rate is the
same in all four simulations. It can also be seen that at different �, different numbers of
dislocations are nucleated in the second grain. It was also found that no annihilation of
dislocations occurred in the second grain during unloading in any case studied and,
therefore, the second grain was not included in Fig. 3b.
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P. Hansson and S. Melin
a b
�
Fig. 3. Number of dislocations N as a function of applied external load � yy during loading (a) and
unloading (b).
The order in which the slip planes in the second grain were activated, according to
Fig. 2b, was also studied. This result is obtained for ��45 �,
and it was found that the
first dislocation for this case nucleated in plane 1, which is the slip plane just below that in
the second grain, coinciding with the slip plane in the first grain (Fig. 2b). The following
order of planes on which nucleation occurred was plane 0, plane, �1, and plane 2. As
seen, nucleation in the second grain first occurs at the slip planes closest to the slip plane
in the first grain before occurring in more distant planes.
Conclusions. The discrete dislocation formulation has been used to investigate the
growth behavior of a short propagating edge crack under fatigue loading conditions.
When investigating the effect of the grain boundary it was found that more dislocations
were nucleated at maximum load in the first grain, holding the crack, when allowing the
plasticity to spread into the next grain, as compared to when restricting the plasticity to
the first grain only. However, the number of dislocations in the first grain also increased
when allowing the spread of the plasticity, resulting in the same crack growth rate for the
simulated cases. It was also found that the dislocations in the second grain first nucleated
on slip planes close to the slip plane in the first grain before continuing in more distant
slip planes.
1. D. S. Suresh, Fatigue of Materials, Second Edition, University Press, Cambridge (1998).
2. F. O. Riemelmoser, R. Pippan, and O. Kolednik, “Cyclic crack growth in elastic plastic solids:
a description in terms of dislocation theory,” Comput. Mech., 20, 139–144 (1997).
3. F. O. Riemelmoser and R. Pippan, “Mechanical reasons for plasticity-induced crack closure
under plane strain conditions,” Fatigue Fract. Eng. Mater. Struct., 21, 1425–1433 (1998).
4. C. Bjerken and S. Melin, “A study of the influence of grain boundaries on short crack growth
during varying load using a dislocation technique,” Eng. Fract. Mech., 71 (15), 2215–2227
(2004).
5. D. R. Askeland, The Science and Engineering of Materials, Third Edition, Stanley Thornes
(Publishers) Ltd (1998).
6. P. Hansson and S. Melin, “Dislocation-based modeling of the growth of a microstructurally
short crack by single shear due to fatigue loading,” Int. J. Fatigue, 27, 347–356 (2005).
7. D. A. Hills, P. A. Kelly, D. N. Dai, and A. M. Korsunsky, Solution of Crack Problems: The
Distributed Dislocation Technique, Kluwer Academic Publisher (1996).
Received 28. 06. 2007
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UDC 539. 4
Mechanical Behavior of Zr-Based Bulk Metallic Glasses
S. Nowak, 1,a P. Ochin, 1,b A. Pasko, 1 S. Guérin, 1 and Y. Champion 1,c
1 ICMPE-CNRS UMR7182, Université Paris, Vitry-sur-Seine, France
a nowak@icmpe.cnrs.fr, b ochin@icmpe.cnrs.fr, c champion@icmpe.cnrs.fr
Bulk metallic glasses have a very high corrosion resistance and mechanical strength. Bulk metallic
glasses show elastic-perfectly plastic behavior with an extended region of elastic strain (�2%). But
at room temperature their macroscopic plasticity is weak even though a local plastic strain is
observed in shear bands. A relaxation analysis allowed studying micro-mechanisms of plastic
deformation and estimating the apparent activation volume (� 2000 Å 3 ).
Keywords: bulk metallic glasses, compression test, stress relaxation, mechanical properties.
Introduction. Amorphous metallic alloys also called metallic glasses are characterized
by absence of atomic long-range order. Bulk metallic glasses (BMG) exhibit a very high
strength (� 1,6 GPa) and elasticity (� 2%). However, at room temperature, they have low
ductility because of the localization of the plastic strain which is concentrated in a few thin
shear bands. Deformation behavior of BMGs is completely different than crystallized metals
(no dislocation). Spaepen [1] and Argon [2] describe the deformation as the result of jumps
of respectively single-atom or group of atoms in “holes” (free volumes) large enough.
Zr-based BMG have a high GFA (Glass Forming Ability) and particularly the alloy
Zr57Cu20Al10Ti8Ni5 which is the studied alloy in this paper.
BMG Synthesis and Characterization. Initially, the five pure elements are melted
by electromagnetic induction heating in a water-cooled copper crucible under He
atmosphere (Fig. 1a). From 20 to 35 g of BMGs are obtained by re-melting using
electromagnetic levitation under He atmosphere and casting into a copper mold (Fig. 1b).
Different shapes of samples are produced, depending on the subsequent use:
20�35�5mm sheets for compression tests, rods with 10 mm diameter for transmission
electron microscopy analysis and wedge shaped samples for the evaluation of the glass
forming ability (GFA).
For compression tests, rectangular shaped samples, 4�4 mm of cross-sectional area
and 6 mm height, were machined and then polished.
X-ray diffraction and TEM analysis were carried out to control the amorphous state
of the as-cast samples (presence of broad diffuse peaks for XRD, and diffuse rings for
TEM).
The glass transition temperature (Tg � 660 K) and the crystallization temperature
(Tx � 719 K) of the alloy were measured using differential scanning calorimeter (DSC)
and the liquidus temperature (Tl � 1156 K) was measured using DTA. Heating rate of
20 K/min was applied for each analysis.
Mechanical Behavior. Uniaxial compression test under quasi-static loading at room
temperature was performed. BMG exhibits a perfect elastic deformation behavior followed
by a catastrophic brittle fracture with no yielding (Fig. 2). The fracture stress is 1634 MPa
and the region of elastic strain is extended (� 2%). Though macroscopic plasticity is low,
local plastic strain is observed in shear bands (Fig. 3).
Typical morphology of the fracture surface of a BMG, at room-temperature in
compression, is shown in Fig. 4. Veins with liquid droplets were observed in the entire
fracture surface. It was demonstrated that shear localization induces a temperature rise
(more than 900�C at the final-fracture moment, i.e., higher than Tl ) and that deformation
is then related to a local decrease of the viscosity in the shear bands [3].
© S. NOWAK, P. OCHIN, A. PASKO, S. GUÉRIN, Y. CHAMPION, 2008
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S. Nowak, P. Ochin, A. Pasko, et al.
a b
Fig. 1 Fig. 2
Fig. 1. (a) water-cooled copper crucible (b) electromagnetic levitation.
Fig. 2. Stress–strain curve of the Zr57Cu20Al10Ni8Ti5 BMG deformed at room temperature at a strain
�5 �1
rate of 210 � s .
Fig. 3 Fig. 4
Fig. 3. View of free surface, parallel to the compression direction, with visible shear bands. Shear
band thickness is about 20 nm [5].
Fig. 4. Fracture surface with veins and liquid droplets (insert).
The fracture angle was measured for two samples: one was 41� (Fig. 5), the other 45�.
These values indicate that BMG follows the Mohr–Coulomb criterion for plastic yielding
in compression. This behavior is observed for many BMG, such as Zr57.4Cu16.4Ni8.2Al10
[4].
Fig. 5. Fractured sample.
Stress Relaxation Analysis. A relaxation test was performed at room temperature to
approach the micromechanisms of deformation. In literature, most experiments were
conducted at temperatures close to T g [1, 6], BMG having homogeneous deformation at
these temperatures. In our experiment, an attempt is made to examine the localized
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deformation in shear bands. Relaxation is a method allowing the measurement of the
rheologic and the mechanistic parameters without failure of the sample and at a
macroscopic scale (in contrast to the nano-indentation investigating confine plasticity).
The sample is loaded with a strain rate of ���
�5 �1
510 � s . The displacement of the
cross head of the testing machine is stopped just before the catastrophic failure of the
sample. The total deformation is remained constant until the end of the experiment
(� 160,000 s). Consequently, since total deformation is the result of plastic and elastic
deformation:
�� �� � � .
(1)
plastic elastic
The shear stress variation as a function of time is plotted in Fig. 6. Three domains
are defined to describe the curve. Between 300 s (onset of the relaxation) and 8000 s, the
stress decreases slowly (�� max � 7 MPa) following the classical logarithmic relation.
Then, after a transitory plateau, the curve globally increases until 100,000 s and finally
stabilizes in the third part.
I. The first domain follows the logarithmic function [7]:
Mechanical Behavior of Zr-Based Bulk Metallic Glasses
Fig. 6. Plot of the shear stress variation as a function of time.
kT � t �
������0�� ln �1�
�,
V � C �
(2)
where � is applied shear stress, � 0 is applied shear stress at the beginning of the
relaxation, t is time, V app is apparent activation volume, C is time factor, k is
Boltzmann constant, and T absolute temperature. V app is the atomic volume involved in
an elementary thermally activated event. At the onset of the relaxation, the slope is almost
infinite and V app equal to zero. Then the curve can be perfectly fitted between 1000 and
3500 s by the logarithmic relation and the activation volume V app is estimated to 2000 Å 3
(corresponding to 150�, where � is the average atomic volume), which is reasonable
compared to high temperature measurement [8].
II. An increase of � is observed, which is probably related to an energy release.
Such behavior is rather unusual. It was verified that it was not in relation with experiment
artifact: stress variations induced by the machine were measured as negligible compared
with the sample relaxation. Moreover, experiments are performed in a room with constant
temperature and the system (sample-machine) dilatation cannot be taken into account to
explain the phenomenon.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 169
app

S. Nowak, P. Ochin, A. Pasko, et al.
So the change between domain I and II could be related to the variations in
micro-structure which is most likely a crystallization in shear bands [9]. At T� Tg, Nieh
et al. [10] consider amorphous phase as a Newtonian fluid and nanocrystalline particles as
having a superplastic behavior. The plastic deformation strain rate is consequently
expressed by
� ( )� � 2
� � 1� f � � f � �( 1�
f ) A�� f B�
,
(3)
plastic v am v cryst v v
where f v is volume fraction of the crystalline phase, A and B are material constants,
�� am and �� cryst strain rates caused by the amorphous and the crystalline phase,
respectively, and � the applied flow stress.
Though experiment is carried out at room temperature, deformation occurring in
shear bands where temperature rises should be described consistently by Eq. (3).
Consequently, the plastic deformation induces a decrease of the applied stress. Nevertheless
the microstructure variation could be at the origin of an internal stress release. The
measured stress which increases globally would be the sum of the internal stress and the
applied stress.
III. Finally, the stress reaches a value threshold, meaning no longer plastic
deformation.
Conclusions. BMGs are produced by rapid cooling of a metallic alloy, avoiding
atomic long-range order. That gives specific properties to the material like no ductility
because of the localization of the plastic strain in shear bands. Stress relaxation allowed
estimating an apparent activation volume associated to a plastic deformation and
observing an evolution of deformation mode involving most likely a partial crystallization
phenomenon.
Acknowledgments. This work was supported by the DGA within the framework of a “Recherche
Exploratoire et Innovation” (REI No. 05C0145) under the contract No. 0634030004707565 for the
PHD of one of the authors (SN). The authors are also grateful to J. L. Bonnentien, A. Valette, and
M.-F. Trichet for technical support.
1. F. Spaepen, Acta Metall., 25, 407 (1977).
2. A. S. Argon, Acta Metall., 27, 47 (1979).
3. B. Yang, P. K. Liaw, G. Wang, et al., Intermetallics, 12, 1265 (2004).
4. R. T. Ott, F. Sanchez, T. Jiao, et al., Metall. Mater. Trans., 37A, 3251 (2006).
5. A. L. G. Y. Zhang, Appl. Phys. Lett., 89, 071907-1 (2006).
6. O. P. Bobrov, V. A. Khonik, K. Kitagawa, and S. N. Laptev, J. Non-Crystalline Solids, 342,
152 (2004).
7. J. Bonneville, P. Späig, J.-L. Martin, Proc. M.R.S. Symp., 364, 369 (1995).
8. M. Bletry, P. Guyot, Y. Brechet, et al., Intermetallics, 12, 1051 (2004).
9. W. H. Jiang, F. E. Pinkerton, and M. Atzmon, Scripta Mater., 48, 1195 (2003).
10. T. G. Nieh, T. Mukai, C. T. Liu, and J. Wadsworth, Scripta Mater., 40, 1021 (1999).
Received 28. 06. 2007
170 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

UDC 539. 4
In-Service Fatigue Fracture Mechanisms in Covered Disks of a TV3-117VK
Helicopter Turbine Engine
A. A. Shanyavskii 1,a and Yu. A. Potapenko 1
1 State Centre for Civil Aviation Flight Safety, Sheremetievo-1, Moscow Region, Russia
a shana@flysafety.msk.ru
In-service propagating fatigue cracks were examined in EI-698VD superalloy thin turbine covered
disks of the first, second, and third stages of a TV3-117VK helicopter engine within service lifes of
200–1800 h. To reveal causes of early crack initiation and estimate a propagation time, metallographic
and fractographic analyses were performed. The sequence of events during fatigue
cracking of the disks was established. A block of striations on the fracture surface was discovered,
which characterized fatigue crack propagation during one flight of a helicopter under different
operating conditions. The number of striations in each block varied over the range of 4–20, being
much more than those used to design covered disks. Fractographic results were used to estimate
fatigue crack growth in covered disks of different stages using data on different operating
conditions of helicopters.
Keywords: fatigue fracture, low-cycle fatigue, turbine, superalloy, striations, damage
mechanisms, aircraft engine, number of flights.
Introduction. In-flight accident of a KA-32 helicopter happened during wood
transportation in Malaysia [1]. The collapse of this helicopter was due to in-flight failure
of a TV3-117VK turbine engine [1]. The time in service of this engine was 1698 h by the
moment of the accident, including 674 h after the last repair. The transportation time was
30–55 min.
The examination of the engine revealed a hole on the top of its right part caused by
the body fracture (Fig. 1). The fracture zone was located in the vicinity of II covered disk
(CD) of the turbine compressor (TC) [2].
The examination of the engine revealed the failed CDs of the II and III stages of the
TC. Both CDs were installed during the last repair. Their time in service was 674 h. The
CD of the first stage was not replaced during the last repair, its operating time was 1710 h.
The results of investigation of fracture surfaces in the failed CDs of the I–III stages
of a collapsed KA-32 helicopter engine and other CDs of TV3-117VK engines (500–1500
flight hours) are reviewed below. The in-flight fatigue fracture mechanism of the CDs is
briefly discussed.
Research Procedure. The in-service cracked CDs of the TC II and III stages of a
TV3-117 engine were statistically analyzed. The analysis has shown that crack initiation
in CDs occurred near the hole 3.6 mm in diameter (Fig. 1), used to position CDs. Cracks
propagating from the hole in the II CD appeared after about 300 h (Fig. 1c). Cracks were
regularly observed after in-service time of more than 400 h. The number of cracked (not
failed) disks increased with time. First cases of III CDs cracking were registered within
600–800 h. The replacement of the III CDs during repair demonstrates the absence of
correlation between the number of cracks and time in service.
Several in-service cracked CDs of the I–III stages of TV3-117VK engines were
chosen for analysis at the moment of their repair after 500–1500 h in service.
All CDs were manufactured from a EI-698VD superalloy. Its chemical composition,
mechanical properties and the ��-phase structure were consistent with recommendations
for a EI-698VD superalloy. The composition of the material (in wt.%) is given in
Table 1.
© A. A. SHANYAVSKII, Yu. A. POTAPENKO, 2008
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 171

A. A. Shanyavskii and Yu. A. Potapenko
Table 1
Recommended and Actual Material Composition of an Alloy for In-Service Failed CDs
Composition
of a EI-698VD alloy
Ni Si Mn Cr Ti Mo Nb
Recommended Residual
content
�0.6 �0.4 13.0–16.0 2.35–2.75 2.80–3.20 1.8–2.2
II CD ditto �0.6 �0.4 15.7 2.57 2.93 2.1
III CD ditto �0.6 �0.4 15.3 2.60 3.07 1.9
a b c
Fig. 1. Overview of a TV3-117VK engine area with the failed zone (a); scheme of the TK of a
TV3-117 engine in the vicinity of a hole (b) with pin (3) oftheII(1) and III (4) CDsoftheII(2) and
III (5) TC stages, and the number of cracked disks vs. in-service lifetime for the II and III CDs (c).
Pieces with detected cracks were cut out from the disks, and the fracture surfaces
were prepared for fractographic analysis on a Zeiss scanning electron microscope (3 nm
resolution).
Research Results for CDs of a In-Flight Collapsed Engine. The five fragments
are representative of the whole range of fracture patterns in the II CD. The analysis of
fracture surfaces demonstrates that fatigue fracture of the II CD mainly occurred in
fragments 2 and 3. Crack propagation at the first stage was directed outward from the
hole, then the crack was growing along the II CD hub (inward). Intensive oxidation of the
fracture surface happened in the inward direction at a distance up to 15 mm.
Fractographic analysis of the II CD fragments revealed that:
(i) crack propagation in the outward direction initiated from one or several origins
located near the hole (Fig. 1);
(ii) on the fracture surface, not far from an origin, striations were observed and they
represented the block of finer striations within 4–20 (Fig. 2);
(iii) fatigue cracks grew in the outward direction but did not reach the edge of a disk,
when the mechanism of the crack growth by the striation formation changed to the
intergranular mechanism of static or quasistatic fracture;
(iv) crack growth in the inward direction was controlled by the mechanism of the
striation formation down to a depth of about 1.5 mm; then the area of striations in the
crack growth direction was gradually reduced, but intergranular cracking was activated,
dominating at a crack depth of more than 3 mm.
Fractographic analysis of the I and III CDs demonstrated that:
(v) crack propagation in the I CDs occurred from several holes, and blocks of fatigue
striations, detected on the fracture surfaces, were similar to those in the II CD (Fig. 2);
(vi) the III CDs displayed only one zone of fatigue fracture from one of the holes
with striation formation in the outward direction.
172 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

In-Service Fatigue Fracture Mechanisms in Covered Disks ...
a b
Fig. 2. Blocks (a) of striations hi in fatigue fracture surface of the I-CD of the in-flight failed engine
and (b) 21 striations in one of these blocks.
Fractographic analysis showed similar fracture behavior of CDs of different stages.
Thus, CD fatigue cracking occurred in a low-cycle fatigue range. The difference in
the number of striations in each block reflects the difference in the number of events
determined by operating conditions of each flight. This problem was discussed earlier [2].
The same pattern was observed on a strip-chart, which registered in-flight power
variations during wood transportation. This fragment, represented a sequence of 21 cycles
of power variations as a result of helicopter height variations.
Therefore, each block of striations was considered as a crack increment during one
flight. Based on this correlation, fatigue crack growth was estimated in terms of the
number of flights for all CDs (Fig. 3).
a b
c
The examination of disks after different times in service allowed the following
conclusions:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 173
h 2
2 �m
Fig. 3. Number of flights, N p , vs. crack length, a, for the I-CD in the inward direction (a) and for
the II-CD after 1057 h in the outward (b) and inward (c) directions. Holes are indicated by numbers.

A. A. Shanyavskii and Yu. A. Potapenko
1) cracks in II CDs originate after minimum 180 flights and their propagation in both
directions from any hole occurs as follows: a crack initiates and grows in the outward
direction, and further after certain delay, a crack propagates inward;
2) in the II CDs, the onset of crack propagation inward occurred after a crack
propagating outward after minimum 170 flights.
Thus, the II-CDs are the first where the fatigue cracks originate after the service time
not less than 180 flights. Then cracks initiate from holes in the outward direction and,
after propagation during minimum 170 flights, they initiate in the inward direction and
grow to the catastrophic fracture.
Discussion. Analysis of CD fracture surfaces gave the following results for disks:
1. The II CD exhibits fatigue cracking with monotonous dependence of striation
spacing on the crack length in both directions from the hole; growth period for the main
crack was about 600 flights outward and 700 flights inward; transition to the mechanism
of intergranular fracture at a crack length of 1.5 mm occurred after 700 flights.
2. The III CD fatigue cracking took place in the outward direction from the hole
during 580 flights.
3. In the I CD, from one of the holes crack propagates more intensively during about
1100 flights, whereas from other holes a crack growth period did not exceed 400 flights.
Crack growth for the II CD was estimated within crack lengths from 1.5 mm to
15 mm, where intergranular fracture was dominant. The discovered dependences of the
number of flights on the crack length for cracks propagating from two holes to a length of
1.5 mm were mathematically approximated. Then these dependences were used to
calculate the number of flights within crack lengths of 1.5–15 mm. The approximations
showed that the crack growth within 1.5–15 mm took place during 420–650 flights.
The minimum duration of the main crack growth to the moment of the catastrophic
fracture of the II CD was 450�420�870 flights. The total time in service of the disk
includes periods of crack initiation and propagation in two directions and is the sum
180�170�870�1220 flights.
Thus, fatigue cracks in the I and II CDs took place after the last repair, but were not
detected. The change of loading conditions for the I CD at the crack depth of about 0.2 mm
was due to its rearrangement during repair (see Fig. 3a, hole No. 1).
It is recommended to improve non-destructive testing of CDs during their repair to
reveal cracks of a length of 0.1–0.3 mm in depth that could not be detected on the disk
side-surface.
1. A. A. Shanyavskiy and Yu. A. Potapenko, Science Works SIAA, 18, 51 (2006).
2. I. A. Birger and B. F. Balashov, Strength of Structural Materials and Components of Aircraft
Engines [in Russian], Mashinostroenie, Moscow (1981).
3. A. A. Shanyavskiy, Tolerable Fatigue Cracking of the Aircraft Components. Synergy in
Engineering Applications [in Russian], Monograph, Ufa (2003).
Received 28. 06. 2007
174 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Ðåôåðàòû
Óìåíî É., Êèíîñèòà Þ., Êèòàìóðà Ò. Ab
initio èññëåäîâàíèÿ èäåàëüíîãî ïðåäåëà ïðî÷íîñòè
íà ñäâèã ïîëèòèïîâ êàðáèäà êðåìíèÿ
íà îñíîâå ôóíêöèîíàëüíîé òåîðèè ïëîòíîñòè
// Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 8–
13.
Âûïîëíåíû ôóíêöèîíàëüíûå ðàñ÷åòû ab
initio ïëîòíîñòè ñ öåëüþ èçó÷åíèÿ èäåàëüíîé
ñäâèãîâîé äåôîðìàöèè ïîëèòèïîâ SiC (3Ñ,
2Í, 4Í, 6Í). Äåôîðìèðîâàíèå êóáè÷åñêèõ è
ãåêñàãîíàëüíûõ ïîëèòàïîâ â îáëàñòè ìàëûõ
äåôîðìàöèé õàðàêòåðèçóåòñÿ óïðóãèìè ñâîéñòâàìè
ñîñòàâëÿþùèõ òåòðàýäðîâ, Si4C. Õàðàêòåð
óêëàäêè â ïîëèòèïàõ îêàçûâàåò âîçäåéñòâèå
íà ëîêàëèçàöèþ äåôîðìàöèé (÷òî
êîððåëèðóåò ñ ïðîôèëåì ýíåðãèè îáîáùåííîãî
äåôåêòà óêëàäêè êàæäîé ïåðåìåùåííîé
ïëîñêîñòè) è èäåàëüíóþ ïðî÷íîñòü íà
ñäâèã. Ñæèìàþùåå ãèäðîñòàòè÷åñêîå íàïðÿæåíèå
ñíèæàåò èäåàëüíóþ ïðî÷íîñòü íà
ñäâèã, ÷òî îòëè÷àåò ïîâåäåíèå ýòèõ
ìàòåðèàëîâ îò ìåòàëëîâ.
Áîìàñ Õ., Êèíöëåð Ð., Êóíîâ Ñ., Ëåâèø Ã.,
Øðåäåð Ð. Çàðîæäåíèå òðåùèí è ïðåäåë
âûíîñëèâîñòè òâåðäûõ ñòàëåé ïðè ìíîãîîñíûõ
öèêëè÷åñêèõ íàãðóçêàõ // Ïðîáë.
ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 14–19.
Èññëåäîâàíû ïðåäåë âûíîñëèâîñòè è ìåõàíèçìû
çàðîæäåíèÿ óñòàëîñòíûõ òðåùèí â
ìíîãîöèêëîâîì ðåæèìå, èñïîëüçóÿ êðóãëûå
îáðàçöû èç ïîäøèïíèêîâîé ñòàëè 52100,
ïîäâåðãàåìûå äåéñòâèþ ïðîäîëüíûõ ñèë è
êðóòÿùèõ ìîìåíòîâ, à òàêæå êîìáèíàöèè
ýòèõ íàãðóçîê. Èñïîëüçîâàëè ãëàäêèå îáðàçöû
è îáðàçöû ñ êîëüöåâûìè íàäðåçàìè ðàäèóñàìè
1,0 è 0,2 ìì. Âëèÿíèå ñðåäíèõ è
ìíîãîîñíûõ íàïðÿæåíèé íà ïðåäåë âûíîñëèâîñòè
ìîæåò áûòü îáúÿñíåíî ñ ó÷åòîì
ìåõàíèçìîâ çàðîæäåíèÿ òðåùèí è ìèêðîìåõàíèêè.
Çàðîæäåíèå òðåùèí ïðîèñõîäèëî
íà îêñèäàõ, êàðáîíèòðèäàõ è íà ïîâåðõíîñòè.
Ìåõàíèçìû çàðîæäåíèÿ òðåùèí ìîãóò
áûòü ñâÿçàíû ñ òèïîì íàãðóçêè: íàãðóçêè
ñ âðàùàòåëüíûìè ãëàâíûìè íàïðÿæåíèÿìè
áîëåå äåñòðóêòèâíû äëÿ íèòðèäîâ, ÷åì
äëÿ îêñèäîâ. Âîçðàñòàþùèå ìàêñèìàëüíûå
íàïðÿæåíèÿ áîëåå îïàñíû äëÿ íèòðèäîâ,
÷åì äëÿ îêñèäîâ, è âûçûâàþò áîëüøèå ïîâðåæäåíèÿ
ïîâåðõíîñòè, ÷åì íèòðèäîâ. Íîðìàëüíûå
íàïðÿæåíèÿ âûçûâàþò áîëüøåå ïîâðåæäåíèå
îêñèäîâ, ÷åì êàñàòåëüíûå íàïðÿ-
æåíèÿ. Ïðåäåëû âûíîñëèâîñòè ðàññ÷èòûâàëè
ñ ïîìîùüþ ìîäèôèöèðîâàííîé ìîäåëè ñëàáîãî
çâåíà, êîòîðàÿ îáúåäèíÿåò çàðîæäåíèå
òðåùèí â îáúåìå è íà ïîâåðõíîñòè ñ ñîîòâåòñòâóþùèìè
êðèòåðèÿìè óñòàëîñòè. Äëÿ
çàðîæäåíèÿ òðåùèí â îáúåìå áûë èñïîëüçîâàí
êðèòåðèé Äàíã Âàíà. Äëÿ êîððåêòíîãî
îïèñàíèÿ êîíêóðèðóþùåãî çàðîæäåíèÿ òðåùèí
íà ïîâåðõíîñòè áûë ïðèìåíåí íîâûé
êðèòåðèé. Ñ ïîìîùüþ ýòîé êîíöåïöèè ìîæíî
ïðåäñêàçàòü ïðåäåë âûíîñëèâîñòè äëÿ íàãðóçîê,
êîòîðûå ñîçäàþò êðèòè÷åñêèå ïëîñêîñòè
è äèàïàçîí â ðàìêàõ îãðàíè÷åííîãî
ðåæèìà êîýôôèöèåíòîâ àñèììåòðèè öèêëà.
Øåñòàê Ï., ×åðíû Ì., Ïîêëóäà ß. Èññëåäîâàíèå
óïðóãèõ ñâîéñòâ ñòðóêòóðû B19’
ñïëàâà NiTi ïðè îäíîîñíîì è ãèäðîñòàòè-
÷åñêîì íàãðóæåíèè ïðè èñïîëüçîâàíèè
ìåòîäà ab initio // Ïðîáë. ïðî÷íîñòè. – 2008.
– ¹ 1. – Ñ. 20–23.
Ïðîâåäåíî èññëåäîâàíèå îäíîîñíîé è ãèäðîñòàòè÷åñêîé
äåôîðìàöèé ìàðòåíñèòíîé
ñòðóêòóðû B19’ ñïëàâà ñ ïàìÿòüþ ôîðìû
NiTi ïî ìåòîäó ðàñ÷åòîâ ab initio. Âåëè÷èíû
îáúåìíîãî ìîäóëÿ óïðóãîñòè, ìîäóëÿ Þíãà
è òåîðåòè÷åñêîé ïðî÷íîñòè ïðè îäíîîñíîì
ðàñòÿæåíèè è ãèäðîñòàòè÷åñêîì íàãðóæåíèè
ðàññ÷èòàíû ïî ðåàêöèè êðèñòàëëà íà ïðèëîæåííûå
äåôîðìàöèè. Èçó÷åí õàðàêòåð èçìåíåíèÿ
óãëà � ñòðóêòóðû B19’ ïî âñåé òðàåêòîðèè
äåôîðìàöèè. Âûïîëíåíî ñîïîñòàâëåíèå
ðàñ÷åòíûõ çíà÷åíèé ìîäóëÿ Þíãà ñ
èìåþùèìèñÿ ýêñïåðèìåíòàëüíûìè ðåçóëüòàòàìè.
Ïîëó÷åííàÿ èíôîðìàöèÿ äîïîëíÿåò è
ðàñøèðÿåò óæå èçâåñòíûå äàííûå î õàðàêòåðèñòèêàõ
ñïëàâà NiTi.
Þðèêîâà À., Mèøêóô É., ×àõ K., Oöåëèê Â.
Ñòðóêòóðíûå èçìåíåíèÿ âñëåäñòâèå ïîëçó-
÷åñòè â àìîðôíîì ñïëàâå Ni–Si–B // Ïðîáë.
ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 24–27.
Èññëåäîâàíî âëèÿíèå îòæèãà ïîä íàïðÿæåíèåì
íà îáðàòèìóþ ñòðóêòóðíóþ ðåëàêñàöèþ
ïîëîñêè àìîðôíîãî ñïëàâà Ni–Si–B.
Èçìåíåíèÿ àìîðôíîé ñòðóêòóðû, âûçâàííûå
ïîëçó÷åñòüþ, èññëåäîâàëèñü ýêñïåðèìåíòàëüíî
ñ èñïîëüçîâàíèåì äèôôåðåíöèàëüíîé
ñêàíèðóþùåé êàëîðèìåòðèè â íåèçîòåðìè-
÷åñêèõ óñëîâèÿõ è äèëàòîìåòðèè. Ïîêàçàíî,
÷òî çíà÷èòåëüíûå èçìåíåíèÿ ýíòàëüïèè è
äëèíû, ñâÿçàííûå ñ îáðàòèìîé ñòðóêòóðíîé
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 175

Ðåôåðàòû
ðåëàêñàöèåé, íàáëþäàþòñÿ ïîñëå ïðåäâàðèòåëüíîé
ïîëçó÷åñòè ïðè ïîâûøåííîé òåìïåðàòóðå.
Ìèøêóô É., ×àõ Ê., Þðèêîâà À., Îöåëèê Â.,
Áåíãóñ Â., Òàáà÷íèêîâà Å. Ðàçðóøåíèå
àìîðôíîé ìåòàëëè÷åñêîé ëåíòû èç
Zr50Ti16.5Cu15Ni18.5 // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 28–31.
Èññëåäîâàíû îñîáåííîñòè äåôîðìèðîâàíèÿ
è ðàçðóøåíèÿ ìàññèâíîãî àìîðôíîãî ìåòàëëà
Zr50Ti16.5Cu15Ni18.5 â âèäå òîíêîé ëåíòû
ïðè èñïûòàíèè íà ðàñòÿæåíèå ïðè êîìíàòíîé
òåìïåðàòóðå. Ðàçðóøåíèå ëîêàëèçóåòñÿ
â ãëàâíîé ïîëîñå ñäâèãà, ïðè ýòîì óãîë ðàçðóøåíèÿ
ìåæäó îñüþ ðàñòÿãèâàþùåãî íàïðÿæåíèÿ
è ïëîñêîñòüþ ðàçðóøåíèÿ áëèçîê
ê45�. Ôðàêòîãðàôè÷åñêèå èññëåäîâàíèÿ ïîêàçàëè,
÷òî ïîâåðõíîñòü èçëîìà àìîðôíîãî
ìåòàëëè÷åñêîãî ñòåêëà ñîñòîèò â îñíîâíîì
èç æèëüíîé ìîðôîëîãèè. Ïðèâåäåíà ñõåìà
òðåõ çîí ìîðôîëîãèè ïîâåðõíîñòè èçëîìà:
îáëàñòü ïîñëåäîâàòåëüíîãî íåïðåðûâíîãî
ñêîëüæåíèÿ (A), ïðåîáëàäàþùàÿ æèëüíàÿ
ñòðóêòóðà (B) è “ðå÷íàÿ” ðÿáü (C).
Äûìà÷åê Ï., Ìèëè÷êà Ê. Èñïûòàíèÿ íà
èçãèá ìàëûõ îáðàçöîâ è èõ ÷èñëåííîå
ìîäåëèðîâàíèå â óñëîâèÿõ ïîñòîÿííîãî
èçãèáàþùåãî óñèëèÿ // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 32–35.
Ñîïîñòàâëÿþòñÿ ðåçóëüòàòû èñïûòàíèé íà
èçãèá ìèíèàòþðíûõ äèñêîâ ïðè ïîñòîÿííîì
óñèëèè è äàííûå ìîäåëèðîâàíèÿ òàêèõ èñïûòàíèé
ìåòîäîì êîíå÷íûõ ýëåìåíòîâ (ÌÊÝ).
Äëÿ èññëåäîâàíèÿ âûáðàíà æàðîïðî÷íàÿ
ñòàëü òèïà CSN 41 5313 (EN 10CrMo9-10).
Èñïûòàíèÿ íà èçãèá ìèíèàòþðíûõ îáðàçöîâ
(ÈÈÌÎ) è íåîáõîäèìûå òðàäèöèîííûå èñïûòàíèÿ
íà ïîëçó÷åñòü ìàññèâíûõ îáðàçöîâ
ïðîâîäèëèñü ïðè òåìïåðàòóðå 873 Ê. Äëÿ
ìîäåëèðîâàíèÿ ïðèìåíÿëè ñòåïåííóþ çàâèñèìîñòü
Íîðòîíà è ýêñïîíåíöèàëüíóþ çàâèñèìîñòü
â ìîäåëè ÌÊÝ äëÿ ñõåìû ÈÈÌÎ.
Ïàðàìåòðû äëÿ îáåèõ çàâèñèìîñòåé áûëè
ïîëó÷åíû èç ñîîòíîøåíèé íàïðÿæåíèÿ è
ìèíèìàëüíîé ñêîðîñòè ïîëçó÷åñòè, óñòàíîâëåííûõ
ïî äàííûì îáû÷íûõ èñïûòàíèé íà
ïîëçó÷åñòü. Ïðè ïîâûøåííûõ íàãðóçêàõ ñòåïåííàÿ
çàâèñèìîñòü Íîðòîíà îáåñïå÷èâàåò
áîëåå áëèçêîå ñîâïàäåíèå ñ ýêñïåðèìåíòàëüíûìè
äàííûìè, à ïðè ìåíüøèõ íàãðóçêàõ
ëó÷øèå ðåçóëüòàòû ïîëó÷åíû ñ èñïîëüçîâàíèåì
ýêñïîíåíöèàëüíîé çàâèñèìîñòè. Èññëåäîâàíèå
ïîäòâåðæäàåò òàêæå ïðîñòóþ ñâÿçü
ìåæäó íàïðÿæåíèåì ïðè îáû÷íûõ èñïûòà-
íèÿõ è óñèëèåì ïðè èñïûòàíèÿõ ìèíèàòþðíûõ
îáðàçöîâ, ÷òî ïðèâîäèò ê èäåíòè÷íîñòè
âåëè÷èíû íàðàáîòêè äî ðàçðóøåíèÿ â îáîèõ
òèïàõ èñïûòàíèé.
Ìèëè÷êà Ê., Äîáåø Ô. Îïèñàíèå êðèâûõ
ïîëçó÷åñòè äëÿ ñïëàâà Mg–4Al–1Ca // Ïðîáë.
ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 36–39.
Âûïîëíåíû èññëåäîâàíèÿ ïîëçó÷åñòè îïòèìèçèðîâàííîãî
ìàãíèåâîãî ñïëàâà AX41 (4
âåñ.% Al, 1 âåñ.% Ca, Mg – áàëàíñ) â òåìïåðàòóðíîì
äèàïàçîíå 343...673 K è óðîâíÿõ
íàïðÿæåíèé 2...200 ÌÏà. Áûëè ïðîâåäåíû
èñïûòàíèÿ íà ïîëçó÷åñòü ïðè ñòóïåí÷àòîì
íàãðóæåíèè ñæèìàþùåé íàãðóçêîé ñ öåëüþ
îïðåäåëåíèÿ çàâèñèìîñòè ñêîðîñòè ïîëçó-
÷åñòè îò íàïðÿæåíèÿ â äèàïàçîíå 10 –9 ...10 –3
ñ –1 äëÿ äàííîé òåìïåðàòóðû. Âñå âûøåóêàçàííûå
çàâèñèìîñòè õîðîøî îïèñûâàëèñü
óðàâíåíèåì Ãàðàôîëî (òèïà sinh) ñ
ïîêàçàòåëåì ñòåïåíè n = 5. Àíàëèç ïàðàìåòðîâ
ýòîãî óðàâíåíèÿ ïîêàçàë, ÷òî ïîëçó-
÷åñòü âî âñåõ ïðîâåäåííûõ ýêñïåðèìåíòàõ
îïðåäåëÿåòñÿ äèôôóçèåé ðåøåòêè. Ïðè íèçêèõ
óðîâíÿõ íàïðÿæåíèé è âûñîêèõ òåìïåðàòóðàõ
îïðåäåëÿþùèì ÿâëÿåòñÿ ìåõàíèçì
âîñõîæäåíèÿ, à ïðè âûñîêèõ óðîâíÿõ íàïðÿæåíèé
è áîëåå íèçêèõ òåìïåðàòóðàõ – ìåõàíèçì
ñêîëüæåíèÿ.  ïðîìåæóòî÷íîì äèàïàçîíå
íàïðÿæåíèé è òåìïåðàòóð íàáëþäàåòñÿ
õàðàêòåðíîå îòêëîíåíèå ýêñïåðèìåíòàëüíûõ
òî÷åê îò ñòåïåííîé çàâèñèìîñòè.
Çàïëåòàë É., Âå÷åò Ñ., Êîãóò ß., Îáðòëèê Ê.
Óñòàëîñòíàÿ äîëãîâå÷íîñòü èçîòåðìè÷åñêè
îòïóùåííîãî êîâêîãî ÷óãóíà â èíòåðâàëå îò
ïðåäåëà ïðî÷íîñòè ïðè ðàñòÿæåíèè äî óñòîé-
÷èâîãî ïðåäåëà âûíîñëèâîñòè // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 40–43.
Ïîëó÷åíà êðèâàÿ óñòàëîñòè àóñòåíèòíîîòïóùåííîãî
êîâêîãî ÷óãóíà (ADI) â
äèàïàçîíå äîëãîâå÷íîñòè, âêëþ÷àÿ îáëàñòè
ìàëîöèêëîâîé è ìíîãîöèêëîâîé óñòàëîñòè
äî 10 8 öèêëîâ.  êà÷åñòâå ïðåäåëüíîãî çíà-
÷åíèÿ óêàçàííîé êðèâîé èñïîëüçóåòñÿ ïðåäåë
ïðî÷íîñòè ïðè ðàñòÿæåíèè. Ïðîâåäåíû
èñïûòàíèÿ íà óñòàëîñòü ïðè ñèììåòðè÷íîì
ðàñòÿæåíèè–ñæàòèè è íà ðàñòÿæåíèå ïðè
êîìíàòíîé òåìïåðàòóðå èçîòåðìè÷åñêè
òåðìîîáðàáîòàííîãî ÷óãóíà ñ øàðîâèäíûì
ãðàôèòîì, ñ äîáàâêàìè ìåäè è íèêåëÿ,
êîòîðûå îêàçûâàþò ïîëîæèòåëüíîå âëèÿíèå
íà ìåõàíè÷åñêèå, òåõíîëîãè÷åñêèå è
óñòàëîñòíûå ñâîéñòâà ADI. Îñóùåñòâëåíà
ïðîâåðêà ñîîòâåòñòâóþùèõ ôóíêöèé äëÿ
îïèñàíèÿ ýêñïåðèìåíòàëüíî îïðåäåëåííûõ
176 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

òî÷åê; âûïîëíåí ðàñ÷åò ïàðàìåòðîâ óêàçàííûõ
ôóíêöèé. Íàèëó÷øèå ðåçóëüòàòû ïîëó-
÷åíû ïðè èñïîëüçîâàíèè ôóíêöèè Ïàëüìãðåíà
è ôóíêöèè, ïðåäëîæåííîé Êîãóòîì è
Âå÷åòîì. Èññëåäîâàíî òàêæå âëèÿíèå ÷àñòîòû
öèêëîâ íàãðóæåíèÿ íà óñòàëîñòíîå ïîâåäåíèå
ðàññìàòðèâàåìîãî ìàòåðèàëà ñ ó÷åòîì
òîãî, ÷òî ÷àñòîòà íàãðóæåíèÿ â ìíîãîöèêëîâîé
îáëàñòè íà äâà ïîðÿäêà ïðåâûøàåò
÷àñòîòó íàãðóæåíèÿ â ìàëîöèêëîâîé
îáëàñòè. Ðàññìîòðåíà òàêæå âîçìîæíîñòü
îòñóòñòâèÿ íåïðåðûâíîñòè â ýêñïåðèìåíòàëüíûõ
äàííûõ íà ó÷àñòêå ìåæäó ìàëîöèêëîâîé
è ìíîãîöèêëîâîé îáëàñòÿìè.
Ñóõàíåê Ï., Øèíäëåð È., Kðàòîõâèë Ï.,
Ãàíóñ Ï. Ñîïðîòèâëåíèå äåôîðìèðîâàíèþ è
ïðîöåññû ñòðóêòóðîîáðàçîâàíèÿ àëþìèíèäîâ
æåëåçà ïðè ãîðÿ÷åé ïðîêàòêå // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 44–47.
Ðàçðàáîòàíû ïðîñòûå ìàòåìàòè÷åñêèå ìîäåëè
çàâèñèìîñòè ñðåäíåãî ýêâèâàëåíòíîãî íàïðÿæåíèÿ
îò òåìïåðàòóðû è äåôîðìàöèè
äëÿ âûáðàííûõ àëþìèíèäîâ æåëåçà. Áûëè
èçó÷åíû è ñðàâíåíû ÷åòûðå îäèíàêîâûå
ïëàâêè, ñîäåðæàùèå 16,5...19,2 âåñ.% Al, è
4 âåñ.% Cr è ðàçëè÷íîå êîëè÷åñòâî òèòàíà è
áîðà. Ïëîñêèå îáðàçöû, ðàññîðòèðîâàííûå
ïî òîëùèíå, ïîäâåðãàëèñü ãîðÿ÷åé ïðîêàòêå.
Ñîïðîòèâëåíèå äåôîðìèðîâàíèþ ðàññ÷èòûâàëè
ïî âåëè÷èíå óñèëèÿ íà âàëêè, îïðåäåëåííîé
ñ èñïîëüçîâàíèåì ëàáîðàòîðíîãî
ïðîêàòíîãî ñòàíà Òàíäåì. Ïðîöåññû ñòðóêòóðîîáðàçîâàíèÿ
èñïûòàííûõ àëþìèíèäîâ
ïîñëå äèíàìè÷åñêîãî âîçäåéñòâèÿ è èõ
ñêëîííîñòü ê òðåùèíîîáðàçîâàíèþ èññëåäîâàëè
ñ èñïîëüçîâàíèåì ìåòàëëîãðàôèè.
Îïèñàíû íàáëþäàâøèåñÿ ðàçëè÷èÿ â ïîâåäåíèè
èñïûòàííûõ àëþìèíèäîâ ïðè äåôîðìèðîâàíèè
è â ñïîñîáíîñòè ê ôîðìîèçìåíåíèþ.
Ñåäëà÷åê ß., Õóìàð À. Àíàëèç ìåõàíèçìîâ
ðàçðóøåíèÿ è êà÷åñòâà ïîâåðõíîñòè êîìïîçèöèîííûõ
ìàòåðèàëîâ ïðè ñâåðëåíèè //
Ïðîáë. ïðî÷íîñòè. – 2008. –¹1.–Ñ.48–51.
Îïðåäåëåíû ìåõàíèçìû âçàèìîäåéñòâèÿ
ìåæäó ñâåðëîì è ìàòåðèàëîì. Èñïûòàíèÿ
ïðîâîäèëè íà ñòåêëîíàïîëíåííîì ïîëèýôèðå
è ýïîêñèêàðáîïëàñòå ñ èñïîëüçîâàíèåì
ðàçëè÷íûõ ñïèðàëüíûõ ñâåðë. Ðåæóùèé
èíñòðóìåíò è îáðàáîòàííûå ïîâåðõíîñòè
èçó÷àëè ñ ïîìîùüþ îïòè÷åñêîé ìèêðîñêîïèè,
ñêàíèðóþùåé ìèêðîñêîïèè è
ïîâåðõíîñòíîé ïðîôèëîìåòðèè, ÷òîáû
âûÿâèòü ïîâðåæäåíèå êîìïîçèöèîííîãî
Ðåôåðàòû
ìàòåðèàëà è èçíîñ èíñòðóìåíòà. Ñðåäè äåôåêòîâ,
âûçâàííûõ ñâåðëåíèåì, íàèáîëåå
ñåðüåçíûì ÿâëÿåòñÿ ðàññëîåíèå êàê íà ïëîñêîñòÿõ
âõîäà, òàê è âûõîäà. Ïðåäëîæåíà ìîäåëü
ïðîãíîçèðîâàíèÿ óñèëèÿ ïîäà÷è ïðè
ñâåðëåíèè áåç ðàññëîåíèÿ.
Çàðèêîâñêàÿ Í. Â., Çóåâ Ë. Á. Ëîêàëèçàöèÿ
ïëàñòè÷åñêîé äåôîðìàöèè è ðàçðóøåíèå
ïîëèêðèñòàëëîâ àëþìèíèÿ // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 52–55.
Èññëåäîâàíî âëèÿíèå ðàçìåðà çåðíà êàê
îñíîâíîãî ïàðàìåòðà ñòðóêòóðû íà ìàêðîëîêàëèçàöèþ
ïëàñòè÷åñêîé äåôîðìàöèè â
ïîëèêðèñòàëëè÷åñêîì àëþìèíèè. Âûïîëíåíà
ïðîâåðêà ìàòåìàòè÷åñêîé çàïèñè óêàçàííîé
çàâèñèìîñòè. Îïðåäåëåíû ïðåäåëüíûå
ñëó÷àè äëÿ îáëàñòåé ìàëûõ è áîëüøèõ ðàçìåðîâ
çåðåí. Ðàññìîòðåíî âëèÿíèå ðàçìåðà
îáðàçöà íà ïåðèîä ìàêðîëîêàëèçàöèè.
Øóêàåâ Ñ., Ãëàäñêèé Ì., Çàõîâàéêî À.,
Ïàíàñîâñêèé Ê. Ìåòîä îöåíêè äîëãîâå÷íîñòè
ìåòàëëè÷åñêèõ ìàòåðèàëîâ ïðè ìàëîöèêëîâîé
óñòàëîñòè â óñëîâèÿõ ìíîãîîñíîãî
íàãðóæåíèÿ // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 56–59.
Ïðåäëîæåí íîâûé ìåòîä îöåíêè óñòàëîñòíîé
äîëãîâå÷íîñòè â óñëîâèÿõ ìíîãîîñíîãî
ðàâíîìåðíîãî è íåðàâíîìåðíîãî íàãðóæåíèÿ,
êîòîðûé îñíîâàí íà ìîäèôèöèðîâàííîì êðèòåðèè
Ïèñàðåíêî–Ëåáåäåâà, ëèíåéíîé ãèïîòåçå
íàêîïëåíèÿ ïîâðåæäåíèé è íåëèíåéíîì
ïîäõîäå Ìýíñîíà. Ïðèâåäåíû ðåçóëüòàòû
èñïûòàíèé òèòàíîâîãî ñïëàâà ÂÒ9 íà ìàëîöèêëîâóþ
óñòàëîñòü ïðè íåðàâíîìåðíîì
ïðîïîðöèîíàëüíîì è íåïðîïîðöèîíàëüíîì
äâóõîñíîì íàãðóæåíèè. Èñïûòàíèÿ ïðîâîäèëèñü
ïðè òðåõ óðîâíÿõ äåôîðìàöèé ïî
êðèòåðèþ Ìèçåñà: 0,6; 0,8; 1,0% ñ ðàçëè÷íûìè
ñî÷åòàíèÿìè ïðîïîðöèîíàëüíîé è
íåïðîïîðöèîíàëüíîé òðàåêòîðèé äåôîðìàöèè.
Âñå èñïûòàíèÿ âûïîëíÿëèñü ïðè êîìíàòíîé
òåìïåðàòóðå. Óñòàíîâëåíî, ÷òî ïðåäëàãàåìûé
ìåòîä ÿâëÿåòñÿ ýôôåêòèâíûì è
ïîçâîëÿåò ó÷èòûâàòü òàêèå ôàêòîðû, êàê âèä
äåôîðìèðîâàííîãî ñîñòîÿíèÿ, òèï òðàåêòîðèè
äåôîðìàöèè è íåðàâíîìåðíîñòü íàãðóæåíèÿ.
Øèíäëåð È., Ñóõàíåê Ï., Ðóø Ñ., Êóáå÷êà Ï.,
Ñîéêà ß., Õåãåð Ì., Ëèøêà Ì., Õëèñíèêîâñêè
Ì. Îöåíêà îáðàçîâàíèÿ ãîðÿ÷èõ òðåùèí â
âûñîêîëåãèðîâàííûõ ñòàëÿõ ìåòîäîì ïðîêàòêè
íà êëèí // Ïðîáë. ïðî÷íîñòè. – 2008. –
¹ 1. – Ñ. 60–63.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 177

Ðåôåðàòû
Ïðåäñòàâëåí íîâûé ìåòîä îïðåäåëåíèÿ ãîðÿ÷èõ
òðåùèí â ìåòàëëè÷åñêèõ ìàòåðèàëàõ,
îñíîâàííûé íà ëàáîðàòîðíîé ìåòîäèêå ïðîêàòêè
íà êëèí è êîìïüþòåðíîé îáðàáîòêå
ðåçóëüòàòîâ. Ýêñïåðèìåíòû âûïîëíÿëè íà
îòîáðàííûõ âûñîêîëåãèðîâàííûõ àâòîìàòíûõ
(ôåððèòíûõ è àóñòåíèòíûõ) ñòàëÿõ íîâîãî
òèïà. Â èñõîäíûõ îáðàçöàõ ôðåçåðîâàëè
V-îáðàçíûå íàäðåçû íà èõ áîêîâîé ñòîðîíå,
÷òî îáëåã÷àëî ðàçâèòèå òðåùèí. Ïîñëå
âûðåçêè îáðàçöîâ èç ïðîêàòàííîãî ìàòåðèàëà
âûïîëíÿëè ìåòàëëîãðàôè÷åñêèé àíàëèç
ìèêðîñòðóêòóðû ñ ïîìîùüþ îïòè÷åñêîé
ìèêðîñêîïèè è àíàëèç òðåùèí ñ ïîìîùüþ
ñêàíèðóþùåé ìèêðîñêîïèè. Ðàçðóøåíèå â
çíà÷èòåëüíîé ìåðå âëèÿëî íà ìèêðîñòðóêòóðó,
âîçíèêøóþ âáëèçè ðàçâèâàþùåéñÿ
òðåùèíû. Âáëèçè òðåùèíû íàáëþäàëîñü
çàìåòíîå èçìåíåíèå çåðåí âñëåäñòâèå ðåêðèñòàëëèçàöèè,
âûçâàííîé íàïðÿæåíèÿìè, è
ïîÿâëåíèÿ çîí äåôîðìèðîâàíèÿ, ñîîòâåòñòâóþùèõ
ïðîêàòàííûì è âûòÿíóòûì ñóëüôèäàì.
Êàê ïðàâèëî, ðàçðóøåíèå âîçíèêàëî çà
ñ÷åò ïëàñòè÷åñêîãî ðàçðûâà ñ âèäèìûìè
ÿìêàìè, âûçâàííîãî îòðûâîì ñóëüôèäîâ îò
ìàòåðèàëà. Îöåíèâàëàñü è ñðàâíèâàëàñü
ñêëîííîñòü èçó÷àåìûõ ñòàëåé ê îáðàçîâàíèþ
ãîðÿ÷èõ òðåùèí.
Áåðêà Ë. Î ìåõàíèêå äåôîðìèðîâàíèÿ è ïðîöåññàõ
äðîáëåíèÿ // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 64–68.
Ìåõàíèêà äðîáëåíèÿ è ðàçðóøåíèÿ ÷àñòèö
ÿâëÿåòñÿ îäíîé èç òðóäíîðàçðåøèìûõ ïðîáëåì
ìàòåðèàëîâåäåíèÿ. Íàïðÿæåííîå ñîñòîÿíèå
îáðàáîòàííûõ ìàòåðèàëîâ çíà÷èòåëüíî
íåîäíîðîäíî, è ïîýòîìó ìåõàíèçìû äåôîðìèðîâàíèÿ
è ðàçðóøåíèÿ ñóùåñòâåííî îòëè-
÷àþòñÿ. Ðàçðàáîòàíû äâà ìåòîäà äëÿ ðåàëèçàöèè
ýòèõ ïðîöåññîâ êàê êâàçèîäíîðîäíîãî
ïåðåõîäà. Ñ ïîìîùüþ óñòðîéñòâà è ìåòîäà,
ðàçðàáîòàííûõ Åíèêîëîïîâûì, òâåðäûé ïîëèìåð
ñàìîïðîèçâîëüíî ïðåîáðàçóåòñÿ â ïîðîøîê.
Àíàëîãè÷íàÿ ñèñòåìà íàãðóæåíèÿ
èñïîëüçóåòñÿ äëÿ ïîëó÷åíèÿ ìåëêîçåðíèñòûõ
ìåòàëëîâ, ïîäîáíî èñïîëüçîâàíèþ
óñòðîéñòâà äëÿ ðàâíîêàíàëüíîãî óãëîâîãî
ïðåññîâàíèÿ, ðàçðàáîòàííîãî Âàëèåâûì.
Îáà ìåòîäà èñïîëüçóþòñÿ â íàñòîÿùåå
âðåìÿ äëÿ ïîëó÷åíèÿ íàíîñòðóêòóðíûõ
ìàòåðèàëîâ. Îáðàçîâàíèå íîâûõ ôèçè÷åñêèõ
ïîâåðõíîñòåé ÿâëÿåòñÿ îáùåé ÷åðòîé îáîèõ
ìåòîäîâ. Îíè ïðåäñòàâëÿþò ñîáîé ñâîáîäíûå
îò ÷àñòèö âåðõíèå ïîâåðõíîñòè, íàäïîâåðõíîñòè
èëè ãðàíèöû çåðåí. Â ñîîòâåòñòâèè
ñ ìåòîäîì Âàëèåâà, òðåáóåòñÿ ïîäà÷à
ýíåðãèè â âèäå ìåõàíè÷åñêîé ðàáîòû, ÷òî
îáû÷íî îñóùåñòâëÿåòñÿ îäíîâðåìåííûì âîçäåéñòâèåì
äàâëåíèÿ è êàñàòåëüíîãî íàïðÿæåíèÿ.
Ïîñêîëüêó îáðàçîâàíèå ñâîáîäíûõ
íàäïîâåðõíîñòåé â íàãðóæåííûõ òâåðäûõ
òåëàõ ÿâëÿåòñÿ ïðåäìåòîì ìåõàíèêè ðàçðóøåíèÿ,
äëÿ ðåøåíèÿ ýòîé çàäà÷è èñïîëüçóåòñÿ
óðàâíåíèå Ãðèôôèòñà.
Êàðîëü÷óê À., Ìàõà Ý. Îáúåìíûé è òî÷å÷íûé
ïîäõîäû ïðè îöåíêå óñòàëîñòíîé äîëãîâå÷íîñòè
â óñëîâèÿõ ñîâìåñòíîãî íàãðóæåíèÿ
ïðè èçãèáå è êðó÷åíèè // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 69–72.
Ïðåäñòàâëåí íîâûé íåëîêàëüíûé ïîäõîä ê
íåðàâíîìåðíîìó ðàñïðåäåëåíèþ íàïðÿæåíèé,
êîòîðûé çàêëþ÷àåòñÿ â ïðèâåäåíèè
íàïðÿæåíèé ê ïðåäñòàâèòåëüíûì ëîêàëüíûì
íàïðÿæåíèÿì â êðèòè÷åñêîé ïëîñêîñòè ïðè
ðàñ÷åòå óñòàëîñòíîé äîëãîâå÷íîñòè. Êàñàòåëüíûå
è íîðìàëüíûå íàïðÿæåíèÿ óñðåäíÿþòñÿ
ïî äâóì ïåðåêðûâàþùèìñÿ ïëîùàäÿì
ðàçëè÷íîãî ðàçìåðà, íàõîäÿùèõñÿ â
êðèòè÷åñêîé ïëîñêîñòè. Ïðîâåäåíî ñðàâíåíèå
ïðåäëàãàåìîãî ìåòîäà ñ òî÷å÷íûì ìåòîäîì
(ïî êðèòè÷åñêîìó ðàññòîÿíèþ), âûïîëíåíà
ïðîâåðêà îáîèõ ìåòîäîâ ïðè èñïûòàíèÿõ
íà óñòàëîñòü â óñëîâèÿõ ñîâìåñòíîãî
íàãðóæåíèÿ ïðè èçãèáå è êðó÷åíèè. Ïðîâåðêà
îñóùåñòâëÿëàñü ïî ïîëó÷åííûì ýêñïåðèìåíòàëüíûì
è ðàñ÷åòíûì çíà÷åíèÿì óñòàëîñòíîé
äîëãîâå÷íîñòè ñ ïðèìåíåíèåì äâóõ
êðèòåðèåâ óñòàëîñòíîãî ðàçðóøåíèÿ ïðè
ñëîæíîì íàïðÿæåííîì ñîñòîÿíèè.
Ìàéîð Ø., Ïàïóãà ß., Õîðíèêîâà ß.,
Ïîêëóäà ß. Ñðàâíåíèå êðèòåðèåâ óñòàëîñòè
ïðè ñîâìåñòíîì èçãèáå è êðó÷åíèè äëÿ
àçîòèðîâàííûõ îáðàçöîâ è îáðàçöîâ â
èñõîäíîì ñîñòîÿíèè // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 73–76.
Èññëåäîâàíà óñòàëîñòíàÿ äîëãîâå÷íîñòü àçîòèðîâàííûõ
â ïëàçìå îáðàçöîâ è èñõîäíûõ
îáðàçöîâ èç íèçêîëåãèðîâàííîé âûñîêîïðî÷íîé
ñòàëè. Èñïûòàíèÿ îáðàçöîâ ïðîâîäèëèñü
ïðè ñèíôàçíîì ñîâìåùåííîì èçãèáå ñ
êðó÷åíèåì. Ïîêàçàíî, ÷òî àçîòèðîâàííûå â
ïëàçìå îáðàçöû îáëàäàþò áîëåå âûñîêîé
óñòàëîñòíîé ñòîéêîñòüþ. Óñòàíîâëåíî, ÷òî
äëÿ îáðàçöîâ â èñõîäíîì ñîñòîÿíèè íàèáîëüøàÿ
òî÷íîñòü ïðîãíîçèðîâàíèÿ óñòàëîñòíîé
äîëãîâå÷íîñòè îáåñïå÷èâàåòñÿ ïðè
èñïîëüçîâàíèè êðèòåðèÿ, ïðåäëîæåííîãî
Ìàê-Äèàðìèäîì. Ñ äðóãîé ñòîðîíû, äëÿ
àçîòèðîâàííûõ îáðàçöîâ íàèáîëåå ïîäõîäÿùèì
îêàçàëñÿ êðèòåðèé Ìàòàêå.
178 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Ìðàçêîâà Ë., Ëàóøìàíí Õ. Êîëè÷åñòâåííûé
ôðàêòîãðàôè÷åñêèé àíàëèç ïîâåðõíîñòåé
óäàðíîãî ðàçðóøåíèÿ ñòàëè R73 // Ïðîáë.
ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 77–80.
Âûïîëíåíû èññëåäîâàíèÿ ìàêðîèçîáðàæåíèé
ïîâåðõíîñòåé ðàçðóøåíèé îáðàçöîâ
Øàðïè èç ñòàëè R73. Ïðè ñïåöèàëüíûõ
óñëîâèÿõ îðèåíòàöèè ïîâåðõíîñòåé ðàçðóøåíèÿ
âèäíû ÿðêèå ó÷àñòêè íà èçîáðàæåíèÿõ,
ñîîòâåòñòâóþùèå ãðàíÿì ñêîëà èëè
ÿìêàì âÿçêîãî ðàçðóøåíèÿ. Ýòè ó÷àñòêè ìîãóò
áûòü èñïîëüçîâàíû â êà÷åñòâå îñíîâíîãî
ýëåìåíòà òåêñòóðû äëÿ îáðàáîòêè èçîáðàæåíèÿ.
Ïîñêîëüêó ýòè ó÷àñòêè íà èçîáðàæåíèÿõ
ÿâëÿþòñÿ íàèáîëåå ÿðêèìè, èõ ìîæíî
îòñåÿòü ïóòåì íàñòðîéêè ïîðîãîâîãî óðîâíÿ
îñâåùåííîñòè. Ðåçóëüòàòû ðàñ÷åòà îòíîñèòåëüíîé
äîëè èõ ïëîùàäè òåñíî êîððåëèðóþò
ñ òåìïåðàòóðîé è ýíåðãèåé óäàðíîãî
ðàçðóøåíèÿ.
Taáà÷íèêîâà E. Ä., Ïîäîëüñêèé A. Â., Áåíãóñ
Â. Ç., Ñìèðíîâ Ñ. Í., ×àõ Ê., Mèøêóô É.,
Ñàèòîâà Ë. Ð., Ñåìåíîâà È. Ï., Âàëèåâ Ð. Ç.
Îñîáåííîñòè ìèêðîñòðóêòóðû ïîâåðõíîñòåé
èçëîìà è íèçêîòåìïåðàòóðíûå ìåõàíè÷åñêèå
ñâîéñòâà ñâåðõìåëêîçåðíèñòîãî ELI-ñïëàâà
Ti–6Al–4V // Ïðîáë. ïðî÷íîñòè. – 2008. –
¹ 1. – Ñ. 81–84.
Èññëåäîâàíû îñîáåííîñòè ìèêðîñòðóêòóðû
ïîâåðõíîñòåé èçëîìà è íèçêîòåìïåðàòóðíûå
ìåõàíè÷åñêèå ñâîéñòâà ñâåðõìåëêîçåðíèñòîãî
ELI-ñïëàâà Ti–6Al–4V, îáðàáîòàííîãî ìåòîäîì
ðàâíîêàíàëüíîãî óãëîâîãî ïðåññîâàíèÿ,
ïðè êâàçèñòàòè÷åñêîì îäíîîñíîì
ðàñòÿæåíèè è ñæàòèè. Ïðîâåäåíî ñðàâíåíèå
çíà÷åíèé ïðåäåëà òåêó÷åñòè è îäíîðîäíîé
äåôîðìàöèè, ïîëó÷åííûõ ïðè òåìïåðàòóðàõ
300, 77 è 4,2 K äëÿ ðàçíûõ ñòðóêòóðíûõ
ñîñòîÿíèé ELI-ñïëàâà Ti–6Al–4V ñ ðàçëè÷íûì
ñðåäíèì ðàçìåðîì çåðíà è ìîðôîëîãèåé
�- è �-ôàç. Èññëåäîâàíî ñòàòèñòè÷åñêîå
ðàñïðåäåëåíèå ðàçìåðîâ ÿìîê íà
ïîâåðõíîñòÿõ èçëîìà ïðè ðàçëè÷íûõ ñòðóêòóðíûõ
ñîñòîÿíèÿõ è òåìïåðàòóðàõ.
Êîíå÷íà Ð., Íèêîëåòòî Äæ., Ìàéåðîâà Â.,
Áàé÷è Ï. Âëèÿíèå àçîòèðîâàíèÿ íà õàðàêòåðèñòèêè
óñòàëîñòè è ìèêðîìåõàíèçìû
ðàçðóøåíèÿ ÷óãóíà ñ øàðîâèäíûì ãðàôèòîì
// Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 85–
88.
Ïðîöåññû ìîäèôèêàöèè ïîâåðõíîñòè âñå
áîëåå øèðîêî ïðèìåíÿþòñÿ äëÿ ïîëíîãî ðàñêðûòèÿ
âîçìîæíîñòåé ìàòåðèàëà â óñëîâèÿõ
Ðåôåðàòû
âûñîêèõ óñòàëîñòíûõ íàãðóçîê, ïîñêîëüêó
íà óñòàëîñòíóþ ïðî÷íîñòü âëèÿåò ñîñòîÿíèå
ïîâåðõíîñòè. Àçîòèðîâàíèå øèðîêî èñïîëüçóþò
äëÿ îáðàáîòêè æåëåçîñîäåðæàùèõ ìàòåðèàëîâ,
ïîñêîëüêó îíî ñîçäàåò ïðî÷íûé
ïîâåðõíîñòíûé ñëîé è ïîâåðõíîñòíûå îñòàòî÷íûå
ñæèìàþùèå íàïðÿæåíèÿ. Óñòàëîñòü
òàêæå ñóùåñòâåííî çàâèñèò îò äåôåêòîâ è
íåîäíîðîäíîñòè. Ïðè àçîòèðîâàíèè ÷óãóíà ñ
øàðîâèäíûì ãðàôèòîì â îòíîñèòåëüíî òîíêîì
óïðî÷íåííîì ñëîå (ïðèìåðíî 300 ìêì)
ïðèñóòñòâóþò øàðîâèäíûå âêëþ÷åíèÿ ãðàôèòà
(äèàìåòð ïîðÿäêà 30 ìêì), äåôåêòû
ëèòüÿ è íåîäíîðîäíàÿ ñòðóêòóðà îñíîâû.
Ðàññìàòðèâàåòñÿ âëèÿíèå àçîòèðîâàíèÿ íà
õàðàêòåðèñòèêè óñòàëîñòè è ìåõàíèçìû ðàçðóøåíèÿ
÷óãóíà. Ñíà÷àëà ïðîâîäèëè ãàçîâîå
àçîòèðîâàíèå ôåððèòíîãî ÷óãóíà è ñèíòåòè-
÷åñêîãî ðàñïëàâà ñ ðàçëè÷íûì ñîäåðæàíèåì
àêòèâíîãî ôåððèòà. Çàòåì âûïîëíÿëè ñòðóêòóðíûé
àíàëèç àçîòèðîâàííûõ ñëîåâ; èñïûòàíèå
íà ñîïðîòèâëåíèå óñòàëîñòè ïóòåì
êðóãîâîãî èçãèáà îáðàçöà; êîíòðîëü ïîâåðõíîñòè
óñòàëîñòíîãî ðàçðóøåíèÿ. Ýôôåêòèâíîñòü
è ðàçáðîñ óñòàëîñòíûõ õàðàêòåðèñòèê
îöåíèâàëè ïóòåì âûáîðî÷íîãî êîíòðîëÿ ïîâåðõíîñòåé
ðàçðóøåíèÿ è èäåíòèôèêàöèè
ìèêðîìåõàíèçìîâ ðàçðóøåíèÿ. Ïîëóýìïèðè÷åñêàÿ
ìîäåëü èñïîëüçóåòñÿ äëÿ îöåíêè
ðåçóëüòàòîâ èñïûòàíèé è îïòèìèçàöèè ïðîöåññà.
Êîâàðèê Î., Ñèãë ß. Ìèêðîñòðóêòóðà è ìîðôîëîãèÿ
ïîâåðõíîñòè èçëîìà ãàçîòåðìè÷åñêèõ
ïîêðûòèé èç òóãîïëàâêèõ ìåòàëëîâ è
êåðàìèêè // Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1.
– Ñ. 89–92.
Èññëåäîâàíû òàêèå õàðàêòåðèñòèêè ìèêðîñòðóêòóðû,
êàê ïîðèñòîñòü, ìîðôîëîãèÿ ÷àñòèö
íàïûëåíèÿ è ðàçìåð çåðíà ãàçîòåðìè-
÷åñêèõ ïîêðûòèé èç êåðàìèêè (Al2O3 è
Cr2O3) è òóãîïëàâêèõ ìåòàëëîâ (W è Mo).
Óñòàíîâëåíî, ÷òî òåõíîëîãèÿ íàïûëåíèÿ
(âûñîêî÷àñòîòíàÿ ïëàçìà, ãàçî- èëè âîäîñòàáèëèçèðîâàííàÿ
ïëàçìà ïîñòîÿííîãî òîêà)
îêàçûâàåò çíà÷èòåëüíîå âëèÿíèå íà ìèêðîñòðóêòóðó
ïîêðûòèé ïðè ðàçëè÷íûõ òåìïåðàòóðàõ
è ñêîðîñòÿõ ñîóäàðåíèÿ ÷àñòèö.  òî
æå âðåìÿ îòìå÷åíà âàæíàÿ ðîëü òåìïåðàòóðû
ïîäëîæêè äëÿ ïîêðûòèé èç òóãîïëàâêèõ
ìåòàëëîâ, íàíåñåííûõ ïðè ðàçëè÷íûõ
òåìïåðàòóðàõ ïîäëîæêè. Âñå èññëåäîâàííûå
ïîêðûòèÿ, êàê ïðàâèëî, ñîäåðæàëè òðåùèíû
âíóòðè íàïûëåííûõ ÷àñòèö, ïîðû è ïîëîñòè
ìåæäó ÷àñòèöàìè, îòäåëüíûå ÷àñòèöû ñ ðàçíûìè
ñòåïåíüþ äåôîðìàöèè è ìåæ÷àñòè÷íîãî
ñïåêàíèÿ, êðèñòàëëèòû, îáðàçîâàâøè-
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 179

Ðåôåðàòû
åñÿ âíóòðè îòäåëüíûõ ÷àñòèö èëè ïðîõîäÿùèå
÷åðåç íåñêîëüêî òàêèõ ÷àñòèö. Ïîêàçàíî,
÷òî âåëè÷èíà è ðàñïðîñòðàíåííîñòü
óêàçàííûõ îñîáåííîñòåé ìèêðîñòðóêòóðû
ïðåäîïðåäåëÿþò ìîðôîëîãèþ ïîâåðõíîñòè
èçëîìà ïîêðûòèé, à òàêæå èõ ìåõàíè÷åñêèå
ñâîéñòâà.
Êàö Þ., Òûìÿê Í., Ãåðáåðèõ Â. Â. Ïðèïîâåðõíîñòíàÿ
ìîäèôèêàöèÿ â ðåçóëüòàòå
âçàèìîäåéñòâèÿ ñ âîäîðîäîì: ãëîáàëüíûé è
ëîêàëüíûé ïîäõîäû // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 93–96.
Ðàññìàòðèâàåòñÿ âçàèìîäåéñòâèå óïðóãîïëàñòè÷åñêîãî
òâåðäîãî âåùåñòâà ñ âîäîðîäîì.
Ñðåäîé ñëóæèò ñâîáîäíûé âîäîðîä îò
âíåøíåãî èëè âíóòðåííåãî èñòî÷íèêà, ÷òî
ñîçäàåò àãðåññèâíûé ýôôåêò. Â ðåçóëüòàòå
ïðîèñõîäèëî ïðèïîâåðõíîñòíîå ñìåùåíèå,
êðîìå íà÷àëà îáðàçîâàíèÿ ìèêðîòðåùèí èëè
èõ ðîñòà è çíà÷èòåëüíîãî ìåæôàçíîãî ðàçóïðî÷íåíèÿ,
÷òî ÿâëÿåòñÿ îñíîâíûìè ïðè÷èíàìè
ïîòåðè ìåõàíè÷åñêîé ïðî÷íîñòè. Äëÿ
âñåñòîðîííåãî èçó÷åíèÿ âíóòðåííåé ñòðóêòóðû
ïîâåðõíîñòè áûëà âûáðàíà ìåòàñòàáèëüíàÿ
àóñòåíèòíàÿ íåðæàâåþùàÿ ñòàëü
316Ë. Îáùèå äàííûå î äåéñòâèè âîäîðîäà
áûëè äîïîëíåíû èíôîðìàöèåé íà íàíîóðîâíå.
Äëÿ ïîëó÷åíèÿ äàííûõ íà íàíîóðîâíå
áûëè èçó÷åíû òîíêèå ïëåíêè Ti/Cu,
ò.å. ïðîâåäåíû èñïûòàíèÿ íà ìàëîì îáúåìå
ìàòåðèàëà. Îáðàçöû îáðàáàòûâàëè âîäîðîäîì
â óñëîâèÿõ íèçêîé ëåòó÷åñòè, à ðåçóëüòàòû
êëàññèôèöèðîâàëè ïî ìåõàíè-
÷åñêîìó îòêëèêó ìåòîäîì êîíòàêòíîé ìåõàíèêè.
Ïðèìåíÿëè íàíîèíäåíòèðîâàíèå è
íåïðåðûâíîå öàðàïàíüå ñ èñïîëüçîâàíèåì
ñêàíèðóþùåé ìèêðîñêîïèè. Ðåçóëüòàòû ëîêàëüíûõ
èññëåäîâàíèé ïîñëóæèëè çíà÷èòåëüíûì
âêëàäîì â îáùèå âûâîäû, âêëþ÷àÿ
çàðîæäåíèå äèñëîêàöèé, ïðèïîâåðõíîñòíóþ
ìîäèôèêàöèþ, íà÷àëî ïëàñòè÷åñêîé ëîêàëèçàöèè
è ìèêðîðàçðóøåíèÿ. Ýôôåêòèâíàÿ
ðàáîòà àäãåçèè â òîíêèõ ñëîÿõ óìåíüøèëàñü,
÷òî ñâèäåòåëüñòâóåò î ñóùåñòâåííîì ñíèæåíèè
ìåõàíè÷åñêèõ ñâîéñòâ, âûðàæàåìîì êîëè÷åñòâåííî.
Ïðåèìóùåñòâà ãëîáàëüíîãî è
ëîêàëüíîãî ïîäõîäîâ ïðè èçó÷åíèè íåðæàâåþùåé
ñòàëè ïîçâîëèëè èñïîëüçîâàòü
ìíîãîóðîâíåâûå ìîäåëè, îïèñûâàþùèå
êîìïëåêñíûå ìèêðîìåõàíè÷åñêèå ïðîöåññû.
Koòàë Â., Ñòîïêà Ï., Ñàéäë Ï., Øâîð÷èê Â.
Èçó÷åíèå òîíêîãî ïîâåðõíîñòíîãî ñëîÿ
ïîëèýòèëåíà ïîñëå ïëàçìåííîé îáðàáîòêè //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 97–
100.
Ïðåäñòàâëåíû ðåçóëüòàòû èçó÷åíèÿ âëèÿíèÿ
ïëàçìû àðãîíà íà ïîâåðõíîñòü ïîëèýòèëåíà
âûñîêîé ïëîòíîñòè. Öåëüþ èññëåäîâàíèÿ
ÿâëÿåòñÿ èçìåíåíèå ïîâåðõíîñòè òàêèì
îáðàçîì, ÷òîáû óâåëè÷èòü âàëåíòíîñòü ìåòàëëà/ïîëèìåðà.
Îáðàçöû ïîäâåðãàëè âîçäåéñòâèþ
ðàçðÿäà ïîñòîÿííîãî òîêà, ïðè
ýòîì âðåìÿ âîçäåéñòâèÿ è ìîùíîñòü ÿâëÿëèñü
ïåðåìåííûìè âåëè÷èíàìè. Äëÿ îïðåäåëåíèÿ
âëèÿíèÿ ïëàçìû èñïîëüçîâàëè
ýëåêòðîííûé ïàðàìàãíèòíûé ðåçîíàíñ
(ÝÏÐ) è ôîòîýëåêòðîííóþ ðåíòãåíîâñêóþ
ñïåêòðîñêîïèþ. Ñìà÷èâàåìîñòü ïîâåðõíîñòè
èçó÷àëè ñ èñïîëüçîâàíèåì ãîíèîìåòðèè.
Ïëàçìåííàÿ îáðàáîòêà âåäåò ê îáðàçîâàíèþ
ðàäèêàëîâ è àêòèâèçàöèè òàêèõ ðåàãåíòîâ,
êàê êèñëîðîä è òàêèì îáðàçîì, çíà÷èòåëüíî
óâåëè÷èâàåòñÿ ñìà÷èâàåìîñòü ïîâåðõíîñòè.
Èññëåäîâàíà ýâîëþöèÿ îáðàáîòàííîé ïîâåðõíîñòè
â ðàçëè÷íûõ ñðåäàõ. Ïðèâåäåíî
ïîäòâåðæäåíèå âëèÿíèÿ ïîâûøåííîé êîíöåíòðàöèè
êèñëîðîäà è ñðåäû íà ãðàäèåíò
êîíöåíòðàöèè â ïîâåðõíîñòíûõ ìîíîñëîÿõ.
Äàííûå ÝÏÐ ñâèäåòåëüñòâóþò î ïîñòåïåííîì
è î÷åíü ìåäëåííîì óìåíüøåíèè êîëè-
÷åñòâà ðàäèêàëîâ íà îáðàáîòàííîé ïîâåðõíîñòè
ïîñëå 2000 ÷. Ïðèâåäåíû òàêæå äàííûå
î ÷àñòè÷íîì ðàñòâîðåíèè îáðàáîòàííîé
ïîâåðõíîñòè â âîäå.
Ïëåõîâ O., Óâàðîâ Ñ., Íåéìàðê O. Òåîðåòè÷åñêîå
è ýêñïåðèìåíòàëüíîå èññëåäîâàíèå
ñîîòíîøåíèÿ ðàññåÿííîé è íàêîïëåííîé
ýíåðãèè â æåëåçå ïðè êâàçèñòàòè÷åñêîì è
öèêëè÷åñêîì íàãðóæåíèè // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 101–104.
Ýêñïåðèìåíòàëüíî èññëåäîâàíî ðàññåÿíèå
ýíåðãèè â ìåòàëëàõ ïðè ïëàñòè÷åñêîì äåôîðìèðîâàíèè
è ðàçðàáîòêå òåðìîäèíàìè-
÷åñêîé ìîäåëè äëÿ èçó÷åíèÿ íàêîïëåíèÿ
íàêëåïà ïðè ïëàñòè÷åñêîì äåôîðìèðîâàíèè
è ðàçðóøåíèè. Ïðåäëàãàåìàÿ ìîäåëü îñíîâàíà
íà ñòàòèñòè÷åñêîì îïèñàíèè êîëëåêòèâíûõ
ñâîéñòâ ìåçîñêîïè÷åñêèõ äåôåêòîâ
è íà ðàçäåëåíèè ïëàñòè÷åñêîé äåôîðìàöèè
íà äâå ÷àñòè (äèññèïàòèâíóþ è îáùóþ).
Îáùàÿ ïëàñòè÷åñêàÿ äåôîðìàöèÿ ðàññìàòðèâàëàñü
êàê íåçàâèñèìàÿ òåðìîäèíàìè-
÷åñêàÿ ïåðåìåííàÿ, ÷òî ïîçâîëèëî îïðåäåëèòü
òåðìîäèíàìè÷åñêèé ïîòåíöèàë ñèñòåìû.
Ïîëó÷åííûå îïðåäåëÿþùèå ñîîòíîøåíèÿ
ïðèìåíèëè äëÿ ÷èñëåííîãî ìîäåëèðîâàíèÿ
ðåçóëüòàòîâ èñïûòàíèé íà ðàñòÿæåíèå
è öèêëè÷åñêèõ èñïûòàíèé. ×èñëåííûå ðåçóëüòàòû
õîðîøî ñîãëàñóþòñÿ ñ ýêñïåðèìåíòàëüíûìè
äàííûìè.
180 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Íåéìàðê O., Ïëåõîâ O., Ïðàóä Â., Óâàðîâ Ñ.
Êîëëåêòèâíûå êîëåáàíèÿ ìíîæåñòâà ìèêðîñäâèãîâ
êàê ìåõàíèçì âîëíû ðàçðóøåíèÿ //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 105–
108.
Ïðåäñòàâëåíû ðåçóëüòàòû òåîðåòè÷åñêèõ è
ýêñïåðèìåíòàëüíûõ èññëåäîâàíèé ÿâëåíèÿ
âîëíû ðàçðóøåíèÿ. Ïðåäëîæåíî îïèñàíèå
ÿâëåíèÿ âîëíû ðàçðóøåíèÿ íà îñíîâå àâòîìîäåëüíîãî
ðåøåíèÿ äëÿ ïëîòíîñòè ìèêðîñäâèãîâ.
Ìåõàíèçìû âîçíèêíîâåíèÿ è ðàñïðîñòðàíåíèÿ
âîëíû ðàçðóøåíèÿ êëàññèôèöèðîâàëè
êàê çàìåäëåííîå ðàçðóøåíèå, ïðè-
÷åì âðåìÿ çàäåðæêè ñîîòâåòñòâîâàëî âðåìåíè
âîçáóæäåíèÿ àâòîìîäåëüíûõ âçðûâíûõ
êîëëåêòèâíûõ êîëåáàíèé âî ìíîæåñòâå
ìèêðîñäâèãîâ. Ýêñïåðèìåíòàëüíîå èññëåäîâàíèå
ìåõàíèçìà âîçíèêíîâåíèÿ è ðàñïðîñòðàíåíèÿ
âîëíû ðàçðóøåíèÿ ïðîâîäèëîñü ñ
èñïîëüçîâàíèåì ðàñïëàâëåííîãî êâàðöåâîãî
ñòåðæíÿ è âêëþ÷àëî èñïûòàíèå ïî ìåòîäó
Òåéëîðà ñ âûñîêîñêîðîñòíûì ôîòîãðàôèðîâàíèåì.
Ïîëó÷åííûå ðåçóëüòàòû ïîäòâåðäèëè
“çàìåäëåííûé” ìåõàíèçì âîçíèêíîâåíèÿ
è ðàñïðîñòðàíåíèÿ âîëíû ðàçðóøåíèÿ.
Ïàíóøêîâà Ì., Òèëëîâà Å., Õàëóïîâà Ì.
Çàâèñèìîñòü ìåõàíè÷åñêèõ ñâîéñòâ ëèòîãî
àëþìèíèåâîãî ñïëàâà AlSi9Cu3 îò åãî
ìèêðîñòðóêòóðû // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 109–112.
Ñïëàâ AlSi9Cu3 ÿâëÿåòñÿ îäíèì èç ìàòåðèàëîâ,
øèðîêî èñïîëüçóåìûõ â äâèãàòåëåñòðîåíèè.
Îí èìååò õîðîøóþ æèäêîòåêó÷åñòü,
îòëè÷íóþ îáðàáàòûâàåìîñòü,
ñðåäíþþ ïðî÷íîñòü è íèçêèé óäåëüíûé âåñ.
Îñíîâíîå âíèìàíèå â äàííîì èññëåäîâàíèè
áûëî íàïðàâëåíî íà èññëåäîâàíèå âëèÿíèÿ
ãîìîãåíèçàöèè íà ìèêðîñòðóêòóðó è ìåõàíè÷åñêèå
ñâîéñòâà ýòîãî ñïëàâà (ïðî÷íîñòü
èñõîäíîãî ìàòåðèàëà R m , òâåðäîñòü HBS).
Îáðàáîòêà ïðîâîäèëàñü ïðè òåìïåðàòóðàõ
505, 515 è 525�C�5�C, äëèòåëüíîñòü
îáðàáîòêè êîëåáàëàñü â ïðåäåëàõ 0...32 ÷ (0,
2, 4, 8, 16 è 32 ÷). Ñïëàâ AlSi9Cu3 ñîäåðæàë
�-ìàòðèöó, ýâòåêòè÷åñêèé êðåìíèé è äðóãèå
ôàçû, áîãàòûå æåëåçîì è ìåäüþ, èìåþùèå
ðàçëè÷íóþ ñòðóêòóðó (èãîëü÷àòóþ,
èåðîãëèôîïîäîáíóþ, àæóðíóþ, ãëûáîîáðàçíóþ
è ò.ï.). Ïîëó÷åííûå ðåçóëüòàòû ïîêàçàëè
ñóùåñòâîâàíèå çàâèñèìîñòè ìåæäó
ìåõàíè÷åñêèìè ñâîéñòâàìè è ìîðôîëîãèÿìè
ýâòåêòè÷åñêîãî êðåìíèÿ è áîãàòîé ìåäüþ
Al–Al2Cu–Si-ôàçû, ïðåîáëàäàþùåé âî âðåìÿ
ãîìîãåíèçàöèè.
Ðåôåðàòû
Âàëåê Ø., Õàóøèëä Ï., Êûòêà Ì. Ìåõàíèçìû
ðàçðóøåíèÿ îáëó÷åííîé íåéòðîíàìè
ñòàëè 15Õ2ÌÔÀ // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 113–116.
Èçó÷åíî âëèÿíèå îáëó÷åíèÿ íà ðàçðóøåíèå
êîðïóñíîé ñòàëè 15Õ2ÌÔÀ. Ïîêàçàíî ðàñïðåäåëåíèå
âêëþ÷åíèé è êàðáèäîâ. Âûïîëíåí
àíàëèç îáðàçöîâ, ðàçðóøåííûõ ïî ìåòîäó
Øàðïè, ñ ïîìîùüþ êîëè÷åñòâåííîé
ôðàêòîãðàôèè. Âûÿâëåíà êîððåëÿöèÿ ìåæäó
ýíåðãèåé çàðîæäåíèÿ òðåùèíû è çîíîé âÿçêîãî
ðàçðóøåíèÿ âáëèçè íàäðåçà. Óñòàíîâëåíî,
÷òî áîëüøàÿ ÷àñòü ýíåðãèè ïîãëîùàåòñÿ
íà ñòàäèè, ïðåäøåñòâóþùåé âîçíèêíîâåíèþ
òðåùèíû ñêîëà. Èññëåäîâàíî ðàñïðåäåëåíèå
ÿìîê âÿçêîãî ðàçðóøåíèÿ íà ïîâåðõíîñòè
îáðàçöîâ Øàðïè. Îöåíåíà çàâèñèìîñòü
ìåæäó ðàñïðåäåëåíèåì ÿìîê è ÷àñòèöàìè
âòîðè÷íûõ ôàç.
Äîáåø Ô., Êðàòîõâèë Ï., Ìèëè÷êà Ê. Ïîëçó-
÷åñòü ïðè ñæàòèè àëþìèíèäà æåëåçà òèïà
Fe3Al ñ äîáàâêàìè Zr // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 117–120.
Èçó÷åíà âûñîêîòåìïåðàòóðíàÿ ïîëçó÷åñòü
àëþìèíèäà æåëåçà òèïà Fe3Al, ëåãèðîâàííîãî
öèðêîíèåì â äèàïàçîíå òåìïåðàòóð
873...1073 Ê. Ñïëàâ ñîäåðæàë (àò.%) 31,5 Al,
3,5 Cr, 0,25 Zr, 0,19 C (îñòàëüíîå Fe). Èñïûòàíèÿ
ïðîâîäèëè â äâóõ ñîñòîÿíèÿõ: â ñîñòîÿíèè
ïîñòàâêè ïîñëå ãîðÿ÷åé ïðîêàòêè è
ïîñëå òåðìîîáðàáîòêè (1423 Ê/2 ÷/âîçäóõ).
Èñïûòàíèÿ íà ïîëçó÷åñòü âûïîëíÿëè ïðè
ïîñòîÿííîé ñæèìàþùåé íàãðóçêå ïðè ñòóïåí÷àòîì
íàãðóæåíèè: íà êàæäîé ñòóïåíè
èñïîëüçîâàëè íàãðóçêó äðóãîé âåëè÷èíû
ïîñëå òîãî, êàê íàñòóïàëà ñòàäèÿ óñòàíîâèâøåéñÿ
ñêîðîñòè ïîëçó÷åñòè. Îïðåäåëåíà ýêñïîíåíòà
íàïðÿæåíèÿ è ýíåðãèÿ àêòèâàöèè
äëÿ ñêîðîñòè ïîëçó÷åñòè, îáñóæäåíû âîçìîæíûå
ìåõàíèçìû ïîëçó÷åñòè ñ ïîçèöèé êîíöåïöèè
ïîðîãîâîãî íàïðÿæåíèÿ. Ðåçêîå óìåíüøåíèå
ýêñïîíåíòû íàïðÿæåíèÿ è ïîðîãîâîãî
íàïðÿæåíèÿ ïðè óâåëè÷åíèè òåìïåðàòóðû
ñâèäåòåëüñòâóåò î òîì, ÷òî íàëè÷èå âòîðè÷íûõ
ôàç ñíèæàåò ñêîðîñòü ïîëçó÷åñòè òîëüêî
ïðè òåìïåðàòóðå 873 Ê. Ïîëó÷åííûå ðåçóëüòàòû
ñðàâíèâàëè ñ äàííûìè äëèòåëüíûõ
èñïûòàíèé íà ïîëçó÷åñòü ïðè ðàñòÿæåíèè,
âûïîëíåííûõ íà òîì æå ñïëàâå.
Ðîçóìåê Ä. Ðîñò òðåùèí â ñòàëè FeP04 ïðè
öèêëè÷åñêîì ðàñòÿæåíèè è ðàçëè÷íîé ôîðìå
íàäðåçîâ ñ ó÷åòîì åå ìèêðîñòðóêòóðû //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 121–
124.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 181

Ðåôåðàòû
Ïðåäñòàâëåíû ýêñïåðèìåíòàëüíûå ðåçóëüòàòû
àíàëèçà çàðîæäåíèÿ è ðàñïðîñòðàíåíèÿ
óñòàëîñòíûõ òðåùèí â ñòàëè FeP04. Èñïûòàíèÿ
âûïîëíåíû íà ïëîñêèõ îáðàçöàõ ïðè
öèêëè÷åñêîì ðàñòÿæåíèè è ïîñòîÿííîì
íîìèíàëüíîì êîýôôèöèåíòå àñèììåòðèè
öèêëà R � 0. Ðàññìîòðåíû ïóòè ðàñïðîñòðàíåíèÿ
òðåùèí, èñõîäÿ èç ìèêðîñòðóêòóðû
ìàòåðèàëà.
Äîáåø Ô., Ïåðåñ Ï., Ìèëè÷êà Ê., Ãàðêåñ Ã.,
Àäåâà Ï. Îöåíêà àíèçîòðîïèè ìåõàíè÷åñêèõ
ñâîéñòâ ìàãíèåâûõ ñïëàâîâ ñ ïîìîùüþ
èñïûòàíèé íà ïîëçó÷åñòü ïðè ñæàòèè //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 125–
128.
Ãëóáîêîå ïîíèìàíèå çàâèñèìîñòè ìåõàíè-
÷åñêèõ ñâîéñòâ îò îðèåíòàöèè âîëîêîí â
ìàòåðèàëàõ, ïîëó÷åííûõ ìåòîäàìè íàïðàâëåííîãî
âîçäåéñòâèÿ, ìîæåò áûòü âàæíûì
ôàêòîðîì â ñîçäàíèè ñòðóêòóðíûõ ýëåìåíòîâ.
Èñõîäÿ èç ýòîãî, èñïûòàíèÿ êîðîòêèõ
îáðàçöîâ íà ïîëçó÷åñòü ïðè ñæàòèè ìîãóò
äàòü ïîëåçíóþ èíôîðìàöèþ. Èñïûòàíèÿ
ïðîâîäèëè íà òðåõ ðàçëè÷íûõ ìàòåðèàëàõ íà
îñíîâå ìàãíèÿ: ÷èñòûé ìàãíèé; êîìïîçèò ñ
ìàãíèåâîé ìàòðèöåé, óïðî÷íåííûé 10 îá.%
òèòàíà; ìàãíèåâûé ñïëàâ WES4. Âñå òðè
ìàòåðèàëà áûëè ïîëó÷åíû ìåòîäàìè ïîðîøêîâîé
ìåòàëëóðãèè è ãîðÿ÷åé ýêñòðóçèè.
Îáðàçöû âûðåçàëè òàêèì îáðàçîì, ÷òîáû èõ
ïðîäîëüíàÿ îñü (ò.å. íàïðàâëåíèå íàïðÿæåíèÿ
ïîëçó÷åñòè ïðè ñæàòèè) è îñü ýêñòðóäèðîâàííîãî
îáðàçöà èìåëè çàäàííûé óãîë.
Äëÿ ÷èñòîãî ìàãíèÿ è Mg–Ti êîìïîçèòà çàâèñèìîñòü
ñêîðîñòè ïîëçó÷åñòè ñóùåñòâåííî
çàâèñèò îò îðèåíòàöèè, îñîáåííî ïðè íåáîëüøîì
îòêëîíåíèè îò îñè ýêñòðóçèè. Íàèáîëüøåå
ñîïðîòèâëåíèå ïîëçó÷åñòè èìåëè
îáðàçöû ñ îñüþ íàïðÿæåíèé, ïàðàëëåëüíîé
îñè ýêñòðóçèè, íàèìåíüøåå – ïðè îòêëîíåíèè
íà 45�–90�. Â ñïëàâå WES4 íå íàáëþäàëîñü
çàâèñèìîñòè îò îðèåíòàöèè. Ïîäîáíîå
ïîâåäåíèå ìîæåò áûòü ñâÿçàíî ñ ìèêðîñòðóêòóðîé
ìàòåðèàëà.
Êàäëåö ß., Äâîðàê Ì. Ïîâåðõíîñòíàÿ îáðàáîòêà
íåðæàâåþùåé ñòàëè X12CrNi 18 8 //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 129–
132.
Îïèñàíà òåõíîëîãèÿ äâóõôàçíîé ïîâåðõíîñòíîé
îáðàáîòêè íåðæàâåþùåé ñòàëè, êîòîðàÿ
áàçèðóåòñÿ íà ïëàçìåííîì àçîòèðîâàíèè
äåòàëè ìèêðîèìïóëüñíîé ïëàçìîé ñ ïîñëåäóþùèì
íàíåñåíèåì íèêåëåâîãî ïîêðûòèÿ
è êîìïîçèòíîé íèêåëü-àëìàçíîé ïëåíêè.
Ïîëó÷åííîå äâóõôàçíîå ïîêðûòèå õàðàêòåðèçóåòñÿ
î÷åíü âûñîêèìè ìåõàíè÷åñêèìè
ñâîéñòâàìè, ò.å. ïîâûøåííîé èçíîñîñòîéêîñòüþ,
íèçêèì êîýôôèöèåíòîì òðåíèÿ è
âûñîêîé òâåðäîñòüþ.
Äûÿ Ä., Ñòðàäîìñêè Ç., Ïèðåê À. Àíàëèç
ìèêðîñòðóêòóðû è ðàçðóøåíèÿ ñîñòàðåííîé
ëèòîé äâóõôàçíîé ñòàëè // Ïðîáë. ïðî÷íîñòè.
– 2008. – ¹ 1. – Ñ. 133–136.
Èññåäîâàíî âëèÿíèå ïîâûøåííîãî ñîäåðæàíèÿ
óãëåðîäà è ïàðàìåòðîâ òåðìîîáðàáîòêè
íà ìèêðîñòðóêòóðó è íåêîòîðûå ñâîéñòâà
ôåððèòîàóñòåíèòíîé ëèòîé äâóõôàçíîé ñòàëè.
Èç ýêñïåðèìåíòàëüíûõ ðåçóëüòàòîâ ñëåäóåò,
÷òî ìèêðîñòðóêòóðà ëèòîé ñòàëè ïîñëå
òåðìè÷åñêîé îáðàáîòêè íà òâåðäûé ðàñòâîð
ñóùåñòâåííî èçìåíÿåòñÿ ïðè ïîâûøåíèè
ñîäåðæàíèÿ óãëåðîäà. Ïðîöåññ ñòàðåíèÿ
ñòàëè ïîñëå òåðìè÷åñêîé îáðàáîòêè íà òâåðäûé
ðàñòâîð ïðèâîäèò ê ïðèìåðíî 20%íîìó
ïîâûøåíèþ òâåðäîñòè è ñíèæåíèþ
óäàðíîé ïðî÷íîñòè â íåñêîëüêî ðàç. Ôðàêòîãðàôè÷åñêèå
èññëåäîâàíèÿ ïîêàçûâàþò, ÷òî
äëÿ ïîâåðõíîñòåé ðàçðóøåíèÿ îáðàçöîâ èç
ñòàëè ñ íèçêèì ñîäåðæàíèåì óãëåðîäà õàðàêòåðíûì
ÿâëÿåòñÿ òðàíñêðèñòàëëèòíûé
âÿçêèé ìèêðîìåõàíèçì ðàçðóøåíèÿ. Ïîâûøåíèå
ñîäåðæàíèÿ óãëåðîäà ñîïðîâîæäàåòñÿ
óìåíüøåíèåì óäåëüíîé äîëè çîí ïëàñòè÷åñêîãî
ðàçðóøåíèÿ è ïðîÿâëåíèåì ñìåøàííîãî
(õðóïêîãî è âÿçêîãî) ðàçðóøåíèÿ îáðàçöîâ.
Ïîñëå ñòàðåíèÿ ñòàëè íàáëþäàëñÿ ëèøü
ñìåøàííûé õàðàêòåð ðàçðóøåíèÿ.
Ñòðàäîìñêè Ç., Äûÿ Ä., Ïèðåê À. Âëèÿíèå
ìîðôîëîãèè êàðáèäîâ íà âÿçêîñòü ðàçðóøåíèÿ
ëèòîé ñòàëè G200CrMoNi4-3-3 // Ïðîáë.
ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 137–140.
Èññëåäóåòñÿ âëèÿíèå íåçíà÷èòåëüíîé ìîäèôèêàöèè
õèìè÷åñêîãî ñîñòàâà ëèòîé ñòàëè
G200CrMoNi4-3-3 íà ìîðôîëîãèþ êàðáèäîâ
è òðåùèíîñòîéêîñòü ìàòåðèàëà. Ñ èñïîëüçîâàíèåì
ðàñ÷åòíîé ïðîãðàììû Termo-Calc
áûëè âûïîëíåíû îöåíêà îáúåìíîé äîëè
êàðáèäíîé ôàçû è ñðàâíèòåëüíûé àíàëèç
ïîëó÷åííûõ ðåçóëüòàòîâ ñ äàííûìè ìèêðîñòðóêòóðíûõ
èññëåäîâàíèé. Òðåùèíîñòîéêîñòü
ëèòîé ñòàëè èññëåäîâàëàñü íà îáðàçöàõ
c êðàåâîé òðåùèíîé, äëÿ êîòîðûõ
îïðåäåëÿëèñü êðèòè÷åñêèå çíà÷åíèÿ êîýôôèöèåíòà
èíòåíñèâíîñòè íàïðÿæåíèé K Q .
Ìåòàëëîãðàôè÷åñêèå è ôðàêòîãðàôè÷åñêèå
èññëåäîâàíèÿ ïîâåðõíîñòåé ðàçðóøåíèÿ ïîçâîëèëè
îïðåäåëèòü ìåõàíèçì òðåùèíîîáðàçîâàíèÿ.
182 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1

Óåìàöó É., Òîêàéè Ê., Îõàøè Ò. Êîððîçèîííàÿ
óñòàëîñòü ýêñòðóçèâíûõ ìàãíèåâûõ
ñïëàâîâ AZ80, AZ61 è AM60 â äèñòèëëèðîâàííîé
âîäå // Ïðîáë. ïðî÷íîñòè. – 2008. –
¹ 1. – Ñ. 141–145.
Ñ èñïîëüçîâàíèåì ìåòîäèêè ñâàðêè òðåíèÿ
áûëè ïîëó÷åíû ñîåäèíåíèÿ äâóõ àëþìèíèåâûõ
ñïëàâîâ: ëèòîãî (AC4CH-T6) è îáðàáîòàííîãî
äàâëåíèåì (A6061-T6). Èññëåäîâàëîñü
âëèÿíèå ìèêðîñòðóêòóðû è ïîñëåòåìïåðàòóðíîé
îáðàáîòêè íà ñîïðîòèâëåíèå
óñòàëîñòè ðàçëè÷íûõ ñâàðíûõ ñîåäèíåíèé.
Öåíòðàëüíàÿ ÷àñòü çîíû ñâàðêè õàðàêòåðèçóåòñÿ
áîëåå íèçêèìè çíà÷åíèÿ òâåðäîñòè ïî
Âèêêåðñó, ÷åì çîíû îñíîâíûõ ìåòàëëîâ, ïðè-
÷åì ìèíèìàëüíûå çíà÷åíèÿ òâåðäîñòè áûëè
çàôèêñèðîâàíû íà ïóòè ïåðåìåùåíèÿ ñâàðî÷íîãî
èíñòðóìåíòà. Ñòàòè÷åñêîå ðàçðóøåíèå
ñâàðíûõ ñîåäèíåíèé ïðè ðàñòÿæåíèè
èìåëî ìåñòî ñî ñòîðîíû îñíîâíîãî ñïëàâà
A6061, ãäå òâåðäîñòü áûëà ìèíèìàëüíà, ïðè-
÷åì ñòàòè÷åñêàÿ ïðî÷íîñòü ñâàðíîãî ñîåäèíåíèÿ
èç ðàçíîðîäíûõ ñïëàâîâ áûëà íèæå,
÷åì ó ñïëàâîâ AC4CH è A6061. Óñòàëîñòíîå
ðàçðóøåíèå èìåëî ìåñòî äëÿ îñíîâíîãî ñïëàâà
AC4CH, ÷òî ñâÿçàíî ñ íàëè÷èåì â íåì
ëèòåéíûõ äåôåêòîâ, ïðè÷åì óñòàëîñòíàÿ
ïðî÷íîñòü ñâàðíîãî ñîåäèíåíèÿ èç ðàçíîðîäíûõ
ñïëàâîâ îêàçàëàñü òàêîé æå, êàê ñïëàâà
AC4CH, íî íèæå, ÷åì ñïëàâà A6061. Ïðèìåíåíèå
ìåòîäèêè ñâàðêè òðåíèåì è ïîñëåòåìïåðàòóðíîé
îáðàáîòêè ïîçâîëèëî ïîâûñèòü
óñòàëîñòíóþ ïðî÷íîñòü ñâàðíûõ ñîåäèíåíèé
ðàçíîðîäíûõ ñïëàâîâ äî óðîâíÿ
îñíîâíîãî ñïëàâà À6061.
Íåçáåäîâà Å., Ôèäëåð Ë., Ìàéåð Ç., Âëàõ Á.,
Êíåñë Ç. Òðåùèíîñòîéêîñòü ìíîãîñëîéíûõ
òðóá // Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. –
Ñ. 146–149.
Ìíîãîñëîéíûå òðóáû, ñîñòîÿùèå èç ðàçëè÷íûõ
ìàòåðèàëîâ, ïîçâîëÿþò ÷àñòè÷íî ïîâûñèòü
ñâîéñòâà ñèñòåì òðóáîïðîâîäîâ è ÷àñòî
ïðèìåíÿþòñÿ íà ïðàêòèêå. Äëÿ îöåíêè äîëãîâå÷íîñòè
òàêèõ òðóá íåîáõîäèìî îïðåäåëèòü
èõ îñíîâíûå ïàðàìåòðû ðàçðóøåíèÿ. Ïðåäñòàâëåí
íîâûé ïîäõîä ê âûïîëíåíèþ òàêîé
îöåíêè. Ïðåäëàãàåòñÿ ñïåöèàëüíûé òèï íåîäíîðîäíîãî
Ñ-îáðàçíîãî îáðàçöà, âûðåçàåìîãî
íåïîñðåäñòâåííî èç òðóáû, äëÿ èññëåäîâàíèÿ
ìåòîäàìè ìåõàíèêè ðàçðóøåíèÿ; âûïîëíåí
÷èñëåííûé àíàëèç è ïðîâåäåíû èñïûòàíèÿ.
Ðàñ÷åò ñîîòâåòñòâóþùèõ çíà÷åíèé K
âûïîëíåí ìåòîäîì êîíå÷íûõ ýëåìåíòîâ. Ïîëó-
÷åíû âåëè÷èíû òðåùèíîñòîéêîñòè ìàòåðèàëà
òðóá èç ïîëèýòèëåíà âûñîêîé ïëîòíîñòè.
Ðåôåðàòû
Óåìàöó É., Òîçàêè ß., Òîêàéè Ê., Íàêàìóðà
Ì. Óñòàëîñòü ñîåäèíåíèé, ïîëó÷åííûõ ñâàðêîé
òðåíèåì, ðàçëè÷íûõ àëþìèíèåâûõ ñïëàâîâ:
ëèòûõ è îáðàáîòàííûõ äàâëåíèåì //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 150–
154.
Èñïûòàíèÿ íà êðóãîâîé èçãèá äëÿ îöåíêè
ñîïðîòèâëåíèÿ óñòàëîñòè ïðîâîäèëè íà âîçäóõå
è â äèñòèëëèðîâàííîé âîäå íà òðåõ
ýêñòðóçèâíûõ ìàãíèåâûõ ñïëàâàõ AZ80,
AZ61 è AM60 ðàçëè÷íîãî õèìè÷åñêîãî ñîñòàâà.
Íà âîçäóõå ñîïðîòèâëåíèå óñòàëîñòè
ïðè âûñîêèõ óðîâíÿõ íàïðÿæåíèé áûëî ïðèìåðíî
îäèíàêîâûì äëÿ âñåõ ñïëàâîâ, ïîñêîëüêó
òðåùèíû çàðîæäàëèñü ó èíòåðìåòàëëè÷åñêèõ
ñîåäèíåíèé Al–Mn, òîãäà êàê
AZ80 ñ íàèáîëüøèì ñîäåðæàíèåì Al èìåë
íàèáîëüøåå ñîïðîòèâëåíèå óñòàëîñòè ïðè
íèçêèõ óðîâíÿõ íàïðÿæåíèé, ÷òî îáúÿñíÿåòñÿ
çàðîæäåíèåì òðåùèí âñëåäñòâèå öèêëè-
÷åñêîé äåôîðìàöèè ñêîëüæåíèÿ â ìèêðîñòðóêòóðå
ìàòðèöû. Â äèñòèëëèðîâàííîé
âîäå ñîïðîòèâëåíèå óñòàëîñòè çíà÷èòåëüíî
ñíèæàëîñü çà ñ÷åò îáðàçîâàíèÿ êîððîçèîííûõ
ÿçâ âî âñåõ ñïëàâàõ, à ðàçëè÷èå â
ñîïðîòèâëåíèè óñòàëîñòè ïðè íèçêèõ óðîâíÿõ
íàïðÿæåíèé îòñóòñòâîâàëî, óêàçûâàÿ íà
òî, ÷òî äîáàâêà Al, óëó÷øàâøàÿ ñîïðîòèâëåíèå
óñòàëîñòè íà âîçäóõå, îêàçûâàëà
îòðèöàòåëüíîå âîçäåéñòâèå íà êîððîçèîííóþ
óñòàëîñòü.
Ìóøàëåê Ð., Õàóøèëä Ï., Cèãë ß., Áåíø ß.,
Ñëàìà ß. Ìåõàíè÷åñêèå ñâîéñòâà è îñîáåííîñòè
ðàçðóøåíèÿ âûñîêîïðî÷íûõ ñòàëåé //
Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 155–
158.
Òîëùèíû ëèñòîâîé âûñîêîïðî÷íîé ñòàëè,
ïðèìåíÿåìîé â àâòîìîáèëüíîé ïðîìûøëåííîñòè,
íå ñîîòâåòñòâóþò òðåáîâàíèÿì ñòàíäàðòíûõ
ìåòîäîâ èñïûòàíèé. Öåëü íàñòîÿùåãî
èññëåäîâàíèÿ – ïðåäëîæèòü ïðèåìëåìóþ
ìåòîäîëîãèþ èñïûòàíèé è ñðàâíåíèòü
ìåæäó ñîáîé òîíêîëèñòîâûå âûñîêîïðî÷íûå
ñòàëåé. Ìèêðîñòðóêòóðó èçó÷àëè ñ ïîìîùüþ
îïòè÷åñêîé è ñêàíèðóþùåé ýëåêòðîííîé
ìèêðîñêîïèè. Äëÿ ñðàâíåíèÿ îñîáåííîñòåé
ðàçðóøåíèÿ òðåõ ðàçëè÷íûõ
ñòàëåé (Docol 1200, M. Multiphase 1200 è
BTR165) èñïîëüçîâàëè ìîäèôèöèðîâàííûé
ìåòîä óäàðíûõ èñïûòàíèé ïî Øàðïè è
ìåòîä îöåíêè âÿçêîñòè ðàçðóøåíèÿ. Áûëè
ïîëó÷åíû êðèâûå ïåðåõîäà èç âÿçêîãî
ñîñòîÿíèÿ â õðóïêîå è êðèâûå ñîïðîòèâëåíèÿ
ðàçðûâó (J�� a).
Ïî âÿçêîñòè ðàçðóøåíèÿ,
çàâèñÿùåé îò òîëùèíû îáðàçöîâ,
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1 183

Ðåôåðàòû
îöåíèâàëè âåëè÷èíó KI c.
Ôðàêòîãðàôè-
÷åñêèé àíàëèç ðàçðóøåííûõ îáðàçöîâ ïîêàçàë,
÷òî âñëåäñòâèå òîíêîé ìèêðîñòðóêòóðû
ñìåøàííîãî ôåððèòà-ìàðòåíñèòà ñîõðàíÿåòñÿ
âÿçêèé ìåõàíèçì ðàçðóøåíèÿ äàæå ïðè
íèçêèõ òåìïåðàòóðàõ (äî �100�C). ßêîáñîí Ë., Ïåðññîí Õ., Ìåëèí Ñ. Èññëåäîâàíèå
in situ ðîñòà óñòàëîñòíîé òðåùèíû
ñ ïîìîùüþ ýëåêòðîííîãî ñêàíèðóþùåãî
ìèêðîñêîïà // Ïðîáë. ïðî÷íîñòè. – 2008. –
¹ 1. – Ñ. 159–162.
Ñêîðîñòü ðîñòà óñòàëîñòíîé òðåùèíû (ÐÓÒ)
îïðåäåëÿåòñÿ ðàçëè÷íûìè ìåõàíèçìàìè,
ðåàëèçóåìûìè â îêðåñòíîñòè âåðøèíû òðåùèíû.
Äëÿ èçó÷åíèÿ ýòèõ ìåõàíèçìîâ è èõ
âëèÿíèÿ íà ñêîðîñòü ÐÓÒ äëÿ ðàçëè÷íûõ
ðåæèìîâ íàãðóæåíèÿ áûëè ïðîâåäåíû èññëåäîâàíèÿ
in situ ñ ïîìîùüþ ýëåêòðîííîãî ñêàíèðóþùåãî
ìèêðîñêîïà. Ìèêðîôîòîãðàôèè,
ïîëó÷àåìûå âî âðåìÿ öèêëè÷åñêîãî íàãðóæåíèÿ,
àíàëèçèðîâàëèñü ñ ïîìîùüþ ìåòîäèêè
îáðàáîòêè èçîáðàæåíèé ñ öåëüþ èçìåðåíèÿ
ïåðåìåùåíèé â îêðåñòíîñòè âåðøèíû
òðåùèíû. Ïîëó÷åííûå ðåçóëüòàòû èñïîëüçîâàëèñü
äëÿ ïîñòðîåíèÿ êðèâûõ ïîäàòëèâîñòè
äëÿ ëþáîé òî÷êè íà ëèíèè òðåùèíû,
îïðåäåëåíèÿ åå ôîðìû è ïîëÿ ïåðåìåùåíèé
âîêðóã âåðøèíû. Ïî äàííîé ìåòîäèêå èññëåäîâàëèñü
ìåõàíèçìû ÐÓÒ, ðåàëèçóåìûå, â
÷àñòíîñòè, ïðè öèêëè÷åñêîì íàãðóæåíèè ñ
ïåðåãðóçêàìè è òåðìîìåõàíè÷åñêîé óñòàëîñòè.
Ïîëó÷åííûå ðåçóëüòàòû ñðàâíèâàëèñü
ñ äàííûìè èçìåðåíèé ïî ìåòîäèêå
ïàäåíèÿ ïîòåíöèàëà. Ïðè ýòîì áûëî óñòàíîâëåíî,
÷òî ðàçíûì óñëîâèÿì íàãðóæåíèÿ
ñîîòâåòñòâóþò ðàçëè÷íûå ìåõàíèçìû ÐÓÒ.
Õàíññîí Ï., Ìåëèí Ñ. Èññëåäîâàíèå âëèÿíèÿ
ãðàíèö çåðåí íà ðàçâèòèå êîðîòêèõ óñòàëîñòíûõ
òðåùèí ñ ïîìîùüþ ìåòîäà äèñêðåòíûõ
äèñëîêàöèé // Ïðîáë. ïðî÷íîñòè. – 2008. –
¹ 1. – Ñ. 163–166.
Âûïîëíåíû èññëåäîâàíèÿ âëèÿíèÿ ãðàíèö
çåðåí ó âåðøèíû êîðîòêîé êðàåâîé òðåùèíû,
ðàñïðîñòðàíÿþùåéñÿ â ÎÖÊ-æåëåçå â
óñëîâèÿõ öèêëè÷åñêîãî íàãðóæåíèÿ. Ïðè
ýòîì èñïîëüçîâàëàñü ìîäåëü, ñî÷åòàþùàÿ
ïîñòàíîâêó çàäà÷è ñ òî÷êè çðåíèÿ äèñêðåòíûõ
äèñëîêàöèé ñ ãðàíè÷íî-ýëåìåíòíûì
ïîäõîäîì, ãäå ãðàíèöà îïèñûâàåòñÿ ñ ïîìîùüþ
ýëåìåíòîâ äèïîëÿ äèñëîêàöèè, à ëîêàëüíàÿ
ïëàñòè÷íîñòü ìîäåëèðóåòñÿ ñ ïîìîùüþ
äèñêðåòíûõ äèñëîêàöèé. Ïðè ýòîì
ïîñòóëèðóåòñÿ, ÷òî ãðàíèöà çåðíà ÿâëÿåòñÿ
íåïðîíèöàåìîé, îäíàêî äèñëîêàöèè, íàõîäÿùèåñÿ
â îêðåñòíîñòè ãðàíèöû çåðíà, ãåíåðèðóþò
âûñîêèå íàïðÿæåíèÿ â ñîñåäíèõ çåðíàõ,
â ðåçóëüòàòå ÷åãî èìååò ìåñòî çàðîæäåíèå
äèñëîêàöèé è ðàñïðîñòðàíåíèå ïëàñòè÷åñêîé
çîíû â ñëåäóþùåå çåðíî.
Íîâàê Ñ., Îøèí Ï., Ïàñêî A., Ãóýðèí Ñ.,
Øàìïèîí ß. Ìåõàíè÷åñêèå õàðàêòåðèñòèêè
âûñîêîïðî÷íûõ ñòåêîë íà îñíîâå öèðêîíèÿ
// Ïðîáë. ïðî÷íîñòè. – 2008. – ¹ 1. – Ñ. 167–
170.
Âûñîêîïðî÷íûå ñòåêëà íà îñíîâå ìåòàëëîâ
èìåþò î÷åíü âûñîêèå õàðàêòåðèñòèêè êîððîçèîííîé
óñòîé÷èâîñòè è ìåõàíè÷åñêîé ïðî÷íîñòè.
Èõ äåôîðìèðîâàíèå ÿâëÿåòñÿ àáñîëþòíî
óïðóãîïëàñòè÷åñêèì ñ ïðîòÿæåííûì
ó÷àñòêîì óïðóãîñòè (� 2%). Îäíàêî ïðè êîìíàòíîé
òåìïåðàòóðå èõ ìàêðîïëàñòè÷íîñòü
ïðîÿâëÿåòñÿ ñëàáî, íåñìîòðÿ íà íàëè÷èå ëîêàëüíûõ
ïëàñòè÷åñêèõ äåôîðìàöèé â ïîëîñàõ
ñêîëüæåíèÿ. Àíàëèç ðåëàêñàöèè íàïðÿæåíèé
ïîçâîëèë èññëåäîâàòü ìèêðîìåõàíèçìû
ïëàñòè÷åñêîãî äåôîðìèðîâàíèÿ è îöåíèòü
çíà÷åíèå îáúåìà àêòèâàöèè (� 2000 A 3 ).
Øàíÿâñêèé À. À., Ïîòàïåíêî Þ. À. Ìåõàíèçìû
óñòàëîñòíîãî ðàçðóøåíèÿ äèñêîâ äâè
ãàòåëÿ âåðòîëåòà ÒÂ3-117ÂÊ ïðè ýêñïëóàòàöèîííûõ
íàãðóçêàõ // Ïðîáë. ïðî÷íîñòè. –
2008. – ¹ 1. – Ñ. 171–174.
Èññëåäîâàíî ðàñïðîñòðàíåíèå óñòàëîñòíûõ
òðåùèí â òîíêèõ äèñêàõ òóðáèíû èç ñóïåðñïëàâà
ÝÈ-689ÂÄ ïåðâîé, âòîðîé è òðåòüåé
ñòóïåíåé äâèãàòåëÿ âåðòîëåòà ÒÂ3-117ÂÊ,
ýêñïëóàòèðóåìûõ â òå÷åíèå 200– 1800 ÷. Äëÿ
èçó÷åíèÿ èñòî÷íèêîâ áûñòðîãî èíèöèèðîâàíèÿ
òðåùèí è îöåíêè äëèòåëüíîñòè ñòàäèè
ðàñïðîñòðàíåíèÿ òðåùèí áûëè âûïîëíåíû
ìåòàëëîãðàôè÷åñêèé è ôðàêòîãðàôè÷åñêèé
àíàëèçû. Óñòàíîâëåíà êèíåòèêà óñòàëîñòíîãî
ðàñòðåñêèâàíèÿ äèñêîâ. Íà ïîâåðõíîñòè ðàçðóøåíèÿ
îáíàðóæåíû áëîêè óñòàëîñòíûõ
áîðîçäîê, êàæäûé èç êîòîðûõ õàðàê òåðèçóåò
ðîñò óñòàëîñòíûõ òðåùèí â òå÷åíèå îäíîãî
ïîëåòà âåðòîëåòà ïðè ðàçëè÷íûõ ðåæèìàõ
ýêñïëóàòàöèè. Êîëè÷åñòâî óñòàëîñòíûõ áîðîçäîê
â êàæäîì áëîêå âàðüèðîâàëîñü îò 4 äî 20,
÷òî çíà÷èòåëüíî âûøå ïðîåêòíîãî óðîâíÿ. Ðåçóëüòàòû
ôðàêòîãðàôè÷åñêèõ èññëåäîâàíèé
èñïîëüçîâàëèñü äëÿ îöåíêè êèíåòèêè ðîñòà
óñòàëîñòíûõ òðåùèí â äèñêàõ ðàçëè÷íûõ
ñòóïåíåé ïî äàííûì äëÿ ðàçëè÷íûõ óñëîâèé
ýêñïëóàòàöèè.
184 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2008, ¹ 1